Two points of law:
Yes, a president can switch parties whilst in the White House. It's never happened per se but John Tyler was kicked out of his party during his term and never 'rejoined' it, effectively being a president with no party affiliation. Political parties aren't mentioned in the Constitution.
As far as the tax return issue, there is no law that states the president must release tax returns. It is expected and traditional that he/she does, but it is not mandated. They do, however, have to complete a financial disclosure form, which Trump did when he became a candidate:
www.nytimes.com/interactive/2016/05/18/us/politics/trump-financial-disclosure.html
Why anyone would believe it's a truthful statement of his assets OR why someone with (allegedly) so much money would be in touch with the common man is beyond me.
As far as Kushner and others 'cleaning up' their internet trail, I find it funny that they just don't seem to understand that the internet is 'forever' and that there are always 'ways' to recover information on a device. I also think it's amusing that they just don't seem to understand how guilty it makes them look when they do so. It just goes back to the Trump mentality of "because I say it is and you have to 'believe me'".
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