1a. if you are short of cash note there are a few things like costal fortresses and city walls out east that you should never need to use (unless you are well on your way to loosing the game).
b. at times you might threaten the allies and instead of tech take the gold, just so that you have that money for units.
This should give you some starting cash.
2. Remember it isn't so bad if you loose some cities to the axis - just sell off as many buildings as you can first.
All that will happen is that you get a lot of partisans the axis get a lot of armies in vulnerable positions and you take the city back when your tanks arrive (ok the city wil be smaller....)
as an added bonus you get to make the game look a bit like it did in history

. Those partisans can be quite useful and would be too expensive to build.
Don't waste units defending cities you expect to loose. but if you do beat a city down to about one pop you can buy it back with a spy and probably get a tank or to in the bargain. Also you can set up your defences at a good city like moscow, as opposed to hving to build city walls closer to the front.
On the other hand you can probably hit back with the tanks fast enough that the axis never really get to pressure your good cities.
3. I tended not to go after stockholm early because to have units there is to not have them on the german front. and for that all I get is one city from a weak civ. Better to either take out the turks or to snach soft cities like those in SE europe or to repel the axis tanks.
when you get the caravans going science will come fast, (maybe you can make a run for stealth remember you wnat the furthest big city that desires the resource) - until then I'd not worry about it at all - let the allies tech for you. allies have weak cities in south west asia and athens so if you can get there it is good.
when you get to england, block scapa flow's production square and then next turn attack them with some decent units.