There is no requirement that visitors to the Schengen area (which Czechia is part of) need to be invited by a citizen or resident.
The standard procedure is that your friend would apply for a visa for a tourist visit on his own behalf and get a visa on the strength of his own circumstances. Then once he arrives he'd be free to visit you or not.
Generally you would only be involved in the visa application if he cannot afford the trip himself and you are good enough friends that you're planning to help with his expenses or to let hims stay in your home. In that case you would need to supply a letter to the consulate that confirms you intend to provide that support, which will help them judge if his budget makes sense. Generally speaking writing such a letter would not give you any legal responsibility (as long as you're truthful in describing what your intentions are).
If he can afford including a hotel in his budget for the days he would be visiting you, it would make his visa application both more straightforward and more likely to succeed to do it that way. That doesn't mean he has to actually stay at that hotel; if he's worried about promising something he might not keep, he could still include hotel expenses in the budget and put a footnote like "for the three days in Prague possibly stay with an online friend instead; arrangements are not finalized yet".
It is also possible, if he mentions meeting up with you as part of his description of his travel plan, that he would like to include a letter from you simply as evidence that he's not making it all up. In that case you can consider writing a short letter that states just the facts -- how you know each other, how long time you've known him, and that you're open to meet up at roughly such-and-such time and location for a few hours/days/whatever. Don't attempt to serve as a character witness for him or sound like you're recommending that he get a visa (the consulate won't care about your recommendation anyway).
Some countries also have some different and more formal way for you to claim legal responsibility for some of the risk of letting your friend in (such as the German Verpflichtungserklärung) -- but it doesn't sound like you are such close friends that you ought to touch that at all. In any case, those things are only for lifting otherwise hopeless visa applications into the "barely scraping by" category. Don't let anyone tell you they are standard for all visitors.
Your friend's offer to send money to you sounds like a bit of a red flag. It sounds a bit too eager to get something specific from you that he shouldn't really need if his story holds up. As far as the visa goes, you're not the one he ought to convince about his finances; the consulate is.