Give advice where to dig in the implementation of https on the server?

Question

Browsers

Hello! Our company has developed an epoll-server (edge-triggered), there are sources, I tried to fasten tls-encryption to it using gnutls, it seems to work (with a lets'encrypt certificate)! I test on browsers, from several clients (3 pcs.) in keepalive mode, that is, the server works pseudo-parallel, it will give a piece of data to one client and then another piece, etc. And all the customers seem to be happy! So, I decided to play around with the mobile browser, and then misunderstandings began, first of all, firefox could not go through the handshake procedure, followed by the mobile browser, the server "kills" connections in case of critical errors from gnutls_handshake (), in some cases, browsers repeat many attempts until will achieve a google handshake, for example, others reach the goal from the first or second round, and still others, firefox stupidly connect, the first time it doesn’t work and more and more the server doesn’t receive anything from it, although the wheel in the browser’s web interface spins for 2-3 minutes after that! What could be the problem? Maybe someone has experience in working with gnutls, maybe there are some subtleties on binding gnutls to a non-blocking socket. Oh, and by the way, a certificate without a certificate revocation chain file, so browsers perceive it as "unverified", the certificate was downloaded by certbot, they say that like chain.pem is just a crl file, but the server swears when you specify it in the binding function to gnutls , I’m generally silent about ocsp (:( In general, I want to hear more conscious thoughts from experienced people. How to hone the handshake function, where to download the crl-file and is it possible to check ocsp (as I understand it, you need a link to some resource on the net)?