Your questions answered 1 for 1
Are there routers that allow the simultaneous connection of over 200 users?
YES – I'm not making product recommendations, so simply search using your favorite search engine. The common brands are Ruckus, Cisco, Aruba, Zyxel etc. Etc.
Does changing the subnt mask give me the opportunity to have more than 255 clients on the network?
YES – see below.
The bandwidth of the Wi-Fi radio allows so many users at the same time?
YES and the more discrete APs have functionality to manage bandwidth.
Can it be solved by multiple access points? I mean a router and 3-5 or more access points?
YES, it would be the normal way to do it. APs are limited to a maximum number of clients because of the limits of the wireless protocol, but routers scale much higher, so a decent router will be enough for 500 users. The number of AP depends on the actual AP you are purchasing.
Is it possible to have a DHCP server to provide the IP addresses of users with 192.168.0.1, for example 192.168.3.255?
YES – very simple – a subnet mask of 255.255.255.0 (means that the last part of the mask can give 0 to 255 numbers, for a total of 256). Apart from this, the .0 and .255 are not used because of the way IP routing works, so you can use it 254. So one is used by the gateway leaving 253 client addresses available.
When the subnet mask is 255.255.0.0, this means that a total of (256 x 256) = 65535 IP addresses is possible and after removing the .0.0 and .255.255 files and one more for the gateway, you have 65532.
Since you are in a subnet behind a firewall, the only limitation I can think of will be placed by the router or AP (domestic ones can usually be limited to the last part at 0, but also in the internal market not all devices impose the limit). Keep in mind, the subnet mask is simply a "limit" of IP addressing and in private networks it is essentially an arbitrary limit.