sous vide vs slow cooking

This is more for slow cooker / crock pot.

If it is single or double meal size and you cut up the meat and other ingredients then you should be fine.

Meal for 4 frozen hard, large pieces, and you are not there to stir it is going to have the bottom more done. You are probably not going to create a food safety issue of any part between 40 F and 140 F for longer than 2 hours.

Pull it before and let it defrost all the way or at least partially in the refrigerator is a much better plan. You would want it defrosted enough that you can spread it out in the pot.

If you are only going to cook a single then get a small slow cooker. Consider two meals and then just refrigerate one - it will be good for 3 days and slow cooker meals tend to reheat nicely.

Can also go the other direction and cook four fresh. Eat one, refrigerate one, and freeze two. Most of the crock meals reheat nicely.

Slow cooker versus sous vide is a bigger question and likely a duplicate.

Can you put a frozen package of food into a slowcooker and can it handle cooking it without needing to defrost the food (even if there's meat will this work)?

I wouldn't risk putting frozen food directly in a slow-cooker. If you are cooking small portions, you could try using the HIGH setting, but it's risky nonetheless. If you choose to use a slow-cooker, I would advise you to incorporate the fridge: leave a day or two's worth of food in the fridge a day before you get cooking, put the rest in the freezer. Then, take food from the fridge rather than the freezer to slow-cook. (Just remember to restock the fridge.)

Slow-cookers generally go up to a max temperature just below boiling (~200 °F). I don't think there are any slow cooker that can't hit at least 175°F (which is roughly the bare minimum needed to soften veggies). (A warm setting will put food around 160°F, but I don't suggest using warm for cooking).

The problem is how long it takes for the slow-cooker to reach these temperatures. I'm assuming your cooker has at least HIGH and LOW settings. According to Crock-Pot, you will hit the upper limit on temperature in about 4 hours on HIGH, and double the time (about 8 hours) on LOW. That's definitely risking it for frozen foods, but for thawed foods it should be fine.

Additionally, if a slow cooker can't handle such a thing, is it possible to do so with sous vide?

Yup, you can do it with sous vide. You don't need to thaw the food beforehand if you go this route (but you could be compromising a little texture if you don't; you would have to test this yourself). The thing about sous vide is that you use water to deliver the heat to the food instead of mostly air, and water is over 20 times more thermally conductive. Furthermore, with a sous vide circulator you get the benefit of convection heating. Just remember to add at least 30 minutes extra time in sous-vide if you are going from frozen. If you want to be extra safe, pre-heat your water bath to the temp you want before putting your food in.

Additionally, what are the pros and cons of using a slow cooker vs using a sous vide machine?

There's a lot that could be said here. I'm biased towards sous vide, as it is much more versatile and precise when you need it to be. You can cook at whatever temperature you want, up to around ~90 C. It does require a bit more research though -- a slow cooker is much simpler to use and setup compared to a sous-vide circulator.

To put it simply: just about anything you can cook in a slow cooker can be cooked in sous-vide (assuming you get a quality nice circulator). The converse isn't true, however. (Not without additional programming and equipment, at least). If you plan to get into cooking I would definitely go the sous-vide route; if you want to keep things extra simple then you could get by with a fridge and crock-pot.

Another thing to note would be the power usage. Slow-cookers win here by a fairly large amount -- they use very little power compared to your standard sous-vide setup. That being said, the difference is much, much smaller if you use a well insulated container for sous-vide, like a cooler.