Who pays for the Development server

I would make them pay for the new server and then build in the price of the development into your costs.

Yeah, you have to always be clear upfront with the clients of your costs and what you charge for and what's included in your price.

For your question, of course I would have the client pay for the server since 1) HE asks for it, and 2) has some old proprietaries software. I do not see how this would benefit more the developer than any other jobs he does.

Same goes for updates, it's up to you to include a certain amount of included updates with the dev costs, it if the updates are to be charged on each event. As long as it's determined in advance, as in upfront.

Lastly, of course if you make updates to the client's server and that causes troubles, IF that is due to his own fault, he's to pay for the extra time you spend to fix HIS glitch, I mean unless you provide time for free...

The key is to be clear UPFRONT all the time. He's to know upfront that if you make updates that breaks things and you need to spend more time fixing his old technologies sh... then he'll be billed. If you think you may have trouble to get paid afterward, then change an upfront amount as a retainer in case of glitches on which you will have to spend time after the update.

Already, the way you sound about him, he does not seem to be an "ideal client" and refusing to pay for you have already done for him, you have a trouble maker client that will always ask for more and never will be willing to pay for it... Personally, and that's me, I would fire him right there if he cannot he grasp how this is important, refuses to recognize the work and to pay for it.

Best regards,
Andy

Have them pay for it. Include the server cost in the price you give him. Any updates or changes that are not part of the project you should charge him for it because your time is not free. If you include the update as part of the project then charge for it as well. I usually help out clients at no cost on small things that don't take much time like 5 or 10 minutes but only for clients that don't complain about prices and are happy to pay for my services when I quote them. It's the 80/20 rule. 20% percent of your clients bring in 80% of your profit. Focus on the 20%.