Camera repair requires a lot more skill than most other endeavors. Sometimes there are traps which can get you during disassembly (like the AE-1 tungsten wire). I don't know this particular camera. You can probably lube and adjust curtain speeds by removing the bottom plate. The other ends of the rollers are on top, with more disassembly required, and the attendant risk. To adjust the speeds, though, you need to be able to read them. We do this with an optical device which measures the open time, and the transit times of both curtains. At speeds above 1/60, or 1/125 for metal shutters, the second curtain starts before the first curtain finishes, so there is a slit that moves across the film. This allows for exposures less than the curtain transit time, but means the two curtain speeds have to match, otherwise there is an exposure gradient. Adjusting speeds would be a challenge without the equipment. Lubrication alone might fix it, though. I don't think you have much to lose if you're careful not cause...

I can't say definitively that your camera doesn't have other problems, but I used to do this kind of work. You have a timing problem. If you got no exposure only at higher speeds than reported, I'd say your second curtain is overtaking the first curtain, a rather common calibration problem. This is generally a pretty accessible adjustment, although you would still need test equipment to do it. But for the SLRs I've seen, 1/30 is the slowest speed at which the first curtain opens all the way before the second curtain starts. I don't see how the second curtain could then overtake at 1/60. This means you have a problem with the shutter escapement, which is a bigger deal. Camera disassembly is a pretty delicate operation. I don't know this model, so I don't know how much disassembly is required to fix it. You need to measure curtain speeds, which requires expensive equipment you don't have, in order to determine the exact problem.

(1) Also, working with lithium-ion battery packs can be quite dangerous. The risk of explosion and fire is no joke.

If you want to avoid this problem in the future, quit putting alkaline batteries in it. They all leak. Use NiMH instead, preferably a premium brand. This will be a big win, since not only will the NiMH cells not leak into your equipment, but they actually have a longer run time in higher-current equipment, such as photo strobes. The higher the current, the greater the advantage over alkaline cells, whose capacity collapses at high current. If you use the flash heavily, you will want maximum capacity (runtime). If only normal use, you will probably want a low self-discharge cell, such as Panasonic Eneloop. I've been using these since 2010 (the same cells, now 13 years old), with zero failures. They have also saved me a great deal of money over that time. You will need a smart charger. Also, be sure not to buy name-brand but low-capacity cells. The Eneloops are 1900 mAH and are low self-discharge. No reason to go any lower than that.

The cells swell, making them difficult to remove. If you can't get purchase on them with needle nose pliers, you'll have to drill a hole into the bottom and remove with a screw or hook. When you clean the contacts, don't use baking soda, as is often suggested. The corrosion from the cells is alkaline, not acidic. vinegar on a Qtip will neutralize it. Then get the vinegar out. Swab it with water or isopropyl alcohol. Don't slop it in, you don't want any of this running into the camera. Alkaline cells should never be used in these cameras. They are inferior in every way, but especially because they always leak, often destroying the equipment. Alkaline cells have very few legitimate uses.

Another strong possibility is the damper control, sometimes called the air diverter. The evaporator fan will always run when the compressor is running, as described above, but this cold air can't just be sent to the refrigerator compartment at all times. If it were, your food would freeze. The temperature has to be regulated. There is a small door between the freezer and refrigerator compartments, with a duct to the evaporator. The damper control uses a capillary tube or a thermistor (in conjunction with a microcontroller) to open or close the door to maintain the proper temperature. Some newer models have dual evaporators instead of this door. I wasn't able to find any technical information on your model, but I don't think yours is one of those.

An additional wrinkle, for others. Some models, at least of the 1278, sometimes have a thinner keyboard flex than is usual. Mine was .007" instead of the .009" of the replacement. The .009" flex WILL NOT fit into the connector. I had to call a dozen Mac repair shops before I found one that knew about this. They were able to provide the proper keyboard. So when you get your new keyboard, check the flex to ensure it fits. Otherwise, you might wind up doing the job twice, as I did.

In normal operation, lithium-ion batteries have four enemies: 1. Time. This is your present concern. Nothing you can do about it. 2. Temperature. High temperature ages the cells. Usually this means don't leave it in your car. 3. Cycles. This is your use profile. Road warriors accumulate a lot of cycles. Not something to obsess about -- you wanted portability. 4. Voltage. In normal operation, this involves high state of charge (high cell voltage), which accelerates aging. It's a bad idea to keep it at that state. Those who use their laptop as a desktop are always on the charger. Fortunately, modern Macs adapt to this and hold at 80% state of charge. But there's another thing, a killer. Very low state of charge -- low cell voltage -- is fatal. You never get here in normal operation, but you can during storage (installed or not), especially if your cells were substantially discharged before you start. You'll find out when you install, because the battery management unit will shoot your battery pack through...

Don't use "good quality" batteries. There are no "good quality" alkaline cells. They all leak, giving you what you have here. Get nickel metal-hydride (NiMH) cells and a smart charger. You probably will want high quality low self-discharge NiMH, like the Sanyo (now Panasonic) eneloop. I've used those for the last ten years and have had zero failures. In principle, NiMH can leak, too, but I've never seen it or heard of anyone who has. I've been using them exclusively for the last 15 years with no damage to equipment, saving a few hundred bucks along the way. I do have a collection of sometimes expensive equipment destroyed by alkalines before I got wise. There are other advantages, including both cost and performance advantages, from using NiMH, but this one tops the list.

Are you sure it's WHITE smoke? That's steam (or, more properly, condensed steam in the exhaust). If it has a blue tinge, that's oil smoke, which would be either blowby or valve stem seals (or possibly an oil gallery leaking across the head). It sounds like there was no smoke beforehand, so it's due to the repair. When you replaced the head gasket the second time, did your pistons look unnaturally clean? You might. be able to smell antifreeze in the exhaust condensate -- kinda sweetish smell. There could also be some sludging in your engine oil. The true color of the smoke is definitive. It's either oil or water and you need to know which to get to first base.