Drastically reduce government spending
No. That's a surefire way to prolong the recession. The private sector is not spending any money right now. If the government decides that it's not going to spend any money either, then the economy completely freezes over.
Depends on which taxes you're talking about. Some taxes should be eliminated or reduced, while others should be increased. The overall level of taxation is a little low, but not so low that it poses an immediate problem. I'm willing to maintain - rather than increase - the overall level of taxation until we recover from the recession.
Payroll taxes should be eliminated entirely, personal exemptions and standard deductions should be expanded, and the EITC should be expanded. On the other hand, gasoline taxes should be much higher than they currently are, as should income taxes on the top earners.
Drastically reduce or eliminate regulations
This is too vague to answer without knowing what regulations you're talking about.
No. Foreign aid represents an insignificant fraction of our national budget, and an even more insignificant fraction of our economy. It keeps our relations good with other countries and can help to solve some of the world's worst problems. I realize that a lot of the money goes into the pockets of African warlords if it isn't managed correctly, but that's no reason to eliminate foreign aid entirely.
Yes, absolutely. That would free up hundreds of billions of dollars a year.
End or reduce welfare programs
No. Again, this would prolong the recession. Herbert Hoover's presidency is not usually considered successful...why would you want to return to those conditions?
Send every individual a stimulus check
It depends what kind of stimulus we're talking about. I'm skeptical that just writing everyone a check will help much...but establishing a public works program, and expanding unemployment insurance and medical care very well might stimulate the economy.
Stop corporate welfare and bailouts
Under normal circumstances I would agree. However, there are some companies that do need to be bailed out in the current economic climate. Specifically financial companies, since they are the backbone of our economy.
Yes. Free trade is essential for a strong economy. This is a point of near-unanimity among economists.