Not sure if I can answer all of those questions, but what I've run into is the 2 year rule that lenders look at. So, if you're trying to get a new mortgage and you have a property that hasn't been rented for 2 years, then they don't count the incoming rent to offset the mortgage payments when calculating your debt to income ratio. I did this and even though I have low debt and good income, it wasn't enough to offset the rental house that hadn't been rented for at least 2 years.
Most banks allow up to 4 mortgages I think, so that shouldn't be an issue. I think the issue will be your debt to income ratios. Maybe look at some smaller local banks that will be more willing to work with you on it instead of the big national banks. You could also refinance that 15 year to a 30 year to reduce your monthly payments and decrease your debt to income.
As far as taxes go, it probably mostly depends on your long term strategy. Are these properties cash flowing properly? You have a lot of option here to include selling soon enough to avoid the capital gains, holding it, selling and rolling proceeds into the 1031 to buy another invesment property, etc. Others will be able to give more advice in this area.