From: Warsaw, Poland
Ok... I am not 100% sure that everything I say is correct, but I am totally sure most of it will be. So I will try to answer Your questions.
1. You can build them as long as You want, prowiding You will have credict to pay and maintandence. Also every single one of them will have impact on Your research - BUT not in a way You may think it will. Your empire has it's research potential. Let's think about it as about scientists which are ready to do research for You. For this example let's agree that Your research potential is 100 (usually it is over 700, but it is only example). That means You have 100 scientists to allocate. First of all - it is not 100 for weapons, 100 for Tech, and 100 for Energy. It is 100 total. So the sum of research points allocated in each branch of science must be lower or equal to Your's empire research potential. So if I will build 1000 energy research stations, and each will give me 120 energy research points, that means I will have 12000 energy research points. But because my empire have only 100 research potential it means that 11900 will be unused, and I will use only 100.
Now... If I have 100 research potential, and I made energy, tech and weapons labolatories in equal numbers than my total research potential will be equally divided betwen all branches [so it will be 33 to weapons, 33 to tech and 34 (this 1 is neglectible, right?) to energy]. It is just like creating places to work for scientist. I may provide them enormus facilities but what good comes from it to me, if I do not have eoungh of them to run it? It is cheaper to build a bit to big facility for them - they are working equally fast and I pay lower maintandence :)
But how building addidional (more than needed) research labs influence researching than? Answer is simple - they are changing proportion. Example - I have total research potential 100. I build weapon lab which gives me 100 weapons research potential and two energy lab which give me 200 energy research potential (let's ignore tech in this example). In this case 100 (our total research potential) will be divided betwen weapon and energy. But energy has to times bigger potential than weapons (200>100). So 100 of total research potential will be with those proportion - 34 for weapons and 66 for energy (I know - 34*2=68, and 68 is more than 66, but this 1 point is neglectible). If You would build now one weapons lab which would provided You with additional 100 points to weapons research potential You would recived an equal proportion (200=200) and Your total research potential would be divaded 50/50. In this way You may influence which branch You want to make more important.
How is total research potential changed during a game? By colonising new planets and growing stronger economy and bigger population. I do not know for sure, but as Your empire grows, total research potential also grows (but much slower).
So to answer Your question 1 - it is very inpractical to spam research centers. Better make sure just that summ of Your weapons, energy and tech potential is not much bigger than total research potential.
I would like to point out that I skipped locations bonuses, gov. bonuses, characters bonuses and racial bonuses. Those are applied afther all mentioned by me earlier calculations are made. So in short they will allowe You to get higher amount of research points than Your total research potential would normally allowed. But one important thing - location bonuses do not stack!
2. I usually have around 5 of each kind (with each giving me 120 to it's research branch). And that is eoungh for very long time of gameplay. More important is that I try to have them more or less equal in proportions.
3. Bonus to research from locations such as black holes do not stack and don't influence research centers. It influence all research branch. And You alweys get the biggest bonus that You managet to secure. Example: I have two weapons research centers over interesting planets - first +13% to weapons, second +27%. I am also about to build another weapon research station over +38% black hole. One would suspect that I have right now +40% to weapons research (13+27=40), and afther I will build third research station I will have total 78% bonus (40+38=78). WRONG!!! Currently I have only +27% because they do not add, but just the biggest one is given. Afther I will build the fird research cender it will be +38% because this will become the biggest bonus.
But all branches are autonomus in this matter.
There is absolutly no point in building more than one research center per interesting location (apart from the fact that if during war enemy will destroy one, You will have still second).
I hope that it was helpfull :)
As for tourism I can not help.
(Oh... Great... Just wonderfull - I was sitting for around 1 hour making this long message only to find out that somebody had a smart idea of giving link to appropriate theard... I am already feeling like a donkey ;))
< Message edited by Modest -- 1/18/2013 1:43:03 AM >