Yes, it should be able to run both of those at the same time. It has two 20 amp outlets. Run those two devices separately, one per outlet, you should be fine. See the information on noise. This gen set may be noisier than you want.

If it is a swamp cooler then yes, if it's a large compressor type air conditioner no, if a small compressor air conditioner then it will probably manage. Borrow your neighbours and see. :-)

Yes. If you can make the carburetor quit leaking

Absolutely. They are used for that all the time. You should be able to use a couple of skill saws at the same time. There are two 20 amp 120VAC outlets on it. Just dont run two saws off one outlet.

No, and it has been recommended you get a spare starting cord in case the one on it breaks. This is a good idea for any emergency generator that's got a pull start.

Sump pumps generally have motors that are 1/2 HP or less and this generator would have no trouble at all.

Most of the small compressors that run on 120VAC and have induction motors as opposed to motors with brushes have very high starting current, though briefly. In the shop I worked in we found that the starting surge could be as high as 35 amps. Thats over twice what the outlet rating is that you plug into. Even a 3000 watt generator with 3500 watt overload potential will have a struggle with that. Think of it this way, when you plug your compressor in the generator is motoring along putting out 120Volts atr zero amps (no load). Suddenly it has to accept a very high load and it almost stops running because it does not yet have the right fuel mixture to manage that load. It's quite a struggle to get up to speed. The best solution, if you need a portable compressor, is to buy a gas powered one from the start. Most have Honda engines on them which start easy and are dependable in the field. Even if you use an oil bath electric compressor from a wall outlet don't use an extension cord. If you must use an extension for some strange reason then make sure it's one that's got very heavy wire on it such as 12 gauge or better yet 10 gauge. You may find it cheaper to just buy more hose. That's what is recommended in all the compressor manuals. Don't use a generator unless is is a really big one of 10KW or more else you are asking for trouble. Good luck!

Yes it does. In the muffler system

Yes and no. Yes, it probably has enough power to run a microwave oven and a toaster but not necessarily at the same time. It will be a bit noisy. If real quiet is what you want then go for one of the 2kw ones made by Honda. They are four times the price of this one but extremely quiet. This one's more bang for the buck.

Fridges and freezers generally don't take a huge amount of power and so a 3000 watt gen set is adequate. Air conditioners come in a couple of basic types. One is a unit called a swamp cooler depending on a fan to move air over a wet mat. Evaporation takes place and cools. The other type is like your freezer or fridge, it has a compressor. The compressor necessary to keep a room cool can take quite a bit of power. Better look at the ratings on it. Not sure what to max out for a 3 KW generator. Remember that starting current on an induction motor is pretty high. If the air conditioner is rated at 1200 watts or less running expect a pulse of 3 times that for start. It sounds like you need one of the bigger gen sets if you want to run all of that simultaneously.