1.) Does anyone even use the bitcoin q / core desktop app anymore?
I actually "
started using it this month"

but it seems that people favor "online clients" these days
Most of those users are probably newcomers and for the veteran users who still prefer using such wallets, it's a trade-off between security
[+ a few other things] and convenience.
5.) Is it any more or less secure using online clients vs having the blockchain fully downloaded?
Online clients/web wallets are always less secure, but that doesn't mean the latter is completely risk-free
[it depends on the situation]!
- Here are a few more risks in addition to ETFbitcoin's comment:
- Some of the web wallets are prone to having display bugs [e.g. zero amount is shown, despite viewing your funded address on explorers] that prevents you from using your funds!
- If a hacker infiltrates their platform, there's a high chance that you'd lose your funds!
- In some/most of the web wallets, you don't actually own any of the funds that you see in your wallet ["not your keys, not your coins"] and if something was to happen to their website [e.g. inaccessible], then you'd not be able to spend your funds on that moment.
I mostly tuned out of all latest updates, releases, security vulnerabilities since around 2015. Is there any news I should be up to speed on?
The following link might come in handy:
Bitcoin Improvement Proposals [scroll down]