Will I have a problem if I am on unemployment benefits and I just filed for my wife?

You will still need to submit an affidavit of support and your tax return(s) even if you are currently on unemployment benefits. To ensure that your wife's case is processed without any delay, you should probably look for a joint sponsor.

First, try to figure out how much will you be paid in unemployment benefits: it might be still enough to keep you above the poverty guideline. If it is not, take a good look at your assets (real estate, savings accounts, IRAs, stocks, bonds, etc., car, jewelry) The rules allow you to rely on your assets for affidavit of support purposes if you are short on income; $5 in assets are equivalent to $1 in income. It might not sound very promising, but, if your income is just a few hundred dollars short of the guideline, the scraped together assets might do the trick. If not, you have 2 options: a) to postpone filing for your wife until you find a new job, or b) to look for a co-sponsor. I would not recommend filing now as if you still have a job: this is dishonest, and is bound to become clear at the interview (where you will have to show a letter from your company confirming your continued employment, and pay stubs for the most recent 2-3 months). You are asking USCIS to believe you that your marriage is real, and that you will take care of your wife so that she would not become a public burden; being caught lying by that agency is not a good idea. Bringing in a co-sponsor after filing the case is, technically, possible, but you will have very hard time justifying it to USCIS unless you had a change in your financial circumstances after you filed the petition.

No, it is not a problem. However, if your wife is already in the US and will be concurrently submitting the I-485, then she will also need the completed affidavit of support from you along with the supporting documentation. If you do not have employment at the moment that can support the income stated on the tax returns, it would be better for you to secure a joint sponsor who will also sign the affidavit of support and submit his/her supporting documentation of income and/or assets. If your wife's case will be processed at the consulate, then you will not need to present the financials until that stage (4-5 months from now) so by then you might have a job and may not need a joint sponsor.

Generally, unemployment benefits is not a problem, per se. You just need to prove your spouse will not be a public charge.

The USCIS might ask about your current job situation, but even if they don't, you're under obligation to disclose any material fact (such as loss of employment) to them... If you are to receive enough income through unemployment to still qualify as a sponsor (money is money, it doesn't matter that it is unemployment income), then you'll be ok. If not, or just to be sure, I would try to find a joint-sponsor for the interview. The joint-sponsor will need to complete a separate I-864, supply proof of immigration status (resident or USC) and provide financial documents (last year's taxes and W-2 and a recent pay stub if employed by another).

You will need a co-sponsor if you have no job now.