Oh baloney. The Chinese have been illegally crossing into America long before Trump said anything.

True - but as soon as the Congress started taking up a bill that could fix that problem, Trump stepped in to stop them from fixing it. Trump didn't cause unlawful Chinese border crossings - but he stopped Congress from trying to find a remedy for it.

Because China is an unfree society, with one-party rule combined with significant repression of human rights, there are a lot of people who can make a prima facie case that they suffer from political persecution within the meaning of the relevant laws governing asylum. Basically, China treats political dissidents pretty brutally - which means that if they make it here, they've got a good shot at passing an initial screening. If you don't want them to be released into the country after that happens, you need Congress to act...and since Trump basically told the GOP not to do anything on border security, there's not much that Biden or the Democrats can do to address the problem.