Are there any restrictions for hachnasat sefer torah? There is an article that says one cannot finish a sefer torah on chol hamoed, restricting for a new torah. But are there any restrictions on hachnasat at any other times, and more importantly if it is used. We will be receiving the sefer torah from a shul on the week of Parshat Korach. Is it for example, an amares ayin to have such a simcha associated with that reading? Importantly, there is a government holiday (July 4th - US Independence Day) that will be used as an occasion to bring people to our community. Is it inappropriate to conflate or associate the simcha with a secular observance (similar to how torah study is forbidden on goyishe holidays)?

There's no problem with doing the hachnasat Sefer Torah on any particular Torah reading (including P. Korach). It's also no problem doing on Jul. 4th, especially when more people can attend then, which even adds to the honor of the Torah. The custom to which you alluded, not to learn Torah is just on one particular gentile holiday, and even that custom is rejected and dismissed by most authorities as wrong, especially today when we don't have to worry about Christian pogroms on that day. In short, these are all no problem.