If someone has suggestions for Physics Stack Exchange website's UI where/how or to whom he should make his suggestions?
You can always ask it here, but for many feature requests the best place is Meta Stack Exchange. Physics Stack Exchange is part of a large family of sites which share the same core engine; as a pretty strong rule of thumb, if your question would be as applicable here as in, say, Gardening & Landscaping Stack Exchange, then the place to ask is the mother meta.
For smallish feature requests, like yours,
I'd like to suggest that for example a little icon be added next to the caption of some of the most frequently used tags (such as: homeworks, Quantum, ...)
this can sometimes be implemented directly as a userscript, and they can eventually make it into SOUP (the Stack Overflow Unofficial Patch) if enough people use them. If you're enough of a coder, you can write such a userscript yourself; if not, you can e.g. ask for the feature on the mother meta and mention that you're open to using a userscript for it, in essence soliciting folks to write one for that purpose.
In your specific case, it requires a bit more finesse, because you want to modify the site in response to the details of the user's history. In this regard, if it is doable via the Stack Exchange API, i.e. if the API can provide the information you need, then yes, a userscript can do it; this does seem to be the case with the tags you've been active in, as well as the top answer tags and top question tags for a user. So happy coding ;-).