Yep, pretty much use any decent synth you can find for sounds in those sections.
Some simple ideas to try for musical feedback buttons:
Load your synth. Choose a preset.
Find the main amp envelope and adjust so ADSR all on zero. Raise decay till you have a quick bleep.
Adjust the ADSR of both AMP and FILTER envelope of synth. Always keeping the ...
At the risk of losing rep, I'm going to go against policy and instead try to dissuade you from embarking on this challenge.
All usability experts agree that websites should make no sounds. It makes for poor website UX. Period.
Notifications should be handled visually only. Or, send the user a notification email and hope their email makes a noise ...
I find, certainly with short notification sounds or even power-upesque sounds, that creating a a small arpeggio works. Put some delay on this, then pitch it up so that it affects the speed also, until you find the sweet spot.
I don't see anything special that couldn't be recreated with almost any virtual analog synthesizer. Simple chords, single notes with delay, small cuts made of pads and processed with phaser/flanger etc.
Try to imitate the sounds that you liked and then you'll catch the basics. I like to use Linplug Albino, it's pretty useful. As for free vsti synths, check ...
Jeez, I'm so late to the party that all the good answers are taken. :-p I'll only expound on what's already been said, or add new perspectives.
I think the most important aspects to work backwards from are A) the brand at play, B) the type of website it is (if business, what vertical), and C) its users. Get ready for Supremely Extreme Generalizations™!
Apologies if this is digging up an old question, but I wanted to contribute my own thoughts and perhaps just add some contrast for anybody else who reads the Q&A.
My first instinct is to ask the question 'why?'. Why do you (or the site owner/ developer/ designer etc) want to use UI SFX? I have a foot in both camps here, so from a web design perspective, ...