Is the meta keywords tag worth filling in?
No. Google stated publicly in 2009 that it does not use the keywords meta tag in ranking, and nothing has changed since. Bing has gone further and indicated it can be a signal of low quality when it is stuffed. The tag is a relic of 1990s search engines that trusted sites to describe themselves, an assumption that survived about ten minutes of contact with spammers. The only lasting effect of filling it in is that it publishes your keyword strategy to anyone who views the source.
Why does Google show a different description than the one I wrote?
Because it prefers a snippet that matches the specific query. Google rewrites meta descriptions in the majority of results, pulling a passage from the page body when that passage answers the search better than your written summary. You cannot prevent this, though you can influence it: a description that closely matches the query intent for your main term is more likely to be used verbatim. Treat the description as your preferred snippet rather than a guaranteed one.
Does the meta description affect rankings?
Not directly, and it has not for many years. It affects click-through rate, which is a different thing and still worth optimising, because a result that is compelling gets clicked and a result that is a keyword list does not. Write it the way you would write a line of ad copy: say what the page gives the reader and why it is worth their click, and put that in the first hundred characters where it will survive truncation.
How long should my title tag be?
Aim for roughly 50 to 60 characters. Google truncates on pixel width rather than character count, at around 600 pixels, so a title full of capitals and wide letters gets cut earlier than one in narrow lowercase. The practical rule is to put the distinguishing information first and the brand name last, because if anything is going to be cut it will be the end. Google also rewrites titles a substantial fraction of the time, most often when yours is repetitive or does not match the page.
Is anything sent to a server when I generate these?
No. The tags are assembled by JavaScript running in your browser. Nothing about your unreleased page titles, URLs, or descriptions is transmitted or stored.