Market centers and their upgrades- what is that a bonus to?
Is there any specific way to increase tourism?
There are two ways: increasing your population or increasing your influence.
The total amount of tourism-income generated depends on the population within the galaxy. Each billion people generate a certain amount of bc, but I don't know the value. The share every race gets of this money depends on their influence. For example, if your race produces 30% of the influence in the galaxy, you will get 30% of the tourism.
A higher population also means more influence and more taxes, making this the more lucrative way. However, a higher population also means, that your approval-rating will be lower. This will bring its one share of problems.
There is also a UP proposal and a couple random events, which will increase tourism, but they are not guaranteed to appear.
Research treaties, what exactly do they do?
If you give the research treaty to another race then they will get 10% of your total research (or you from them, if you got their treaty). You don't loose the research though. Sharing your treaty also increases your diplomatic relations with that race, making it easier to get an alliance with them.
However, there are some downsides. The first is, that you can share your treaty only with one race. The second is, that, if you declare war on a race you're sharing your treaty with, you'll get permanently branded as an untrustworthy bastard by everyone, which can make diplomatic negotiations pretty hard.