In terms of being allowed, mods have been discussed openly on these forums since the game came out. No moderator has ever said that the devs don't allow it. The devs do allow console commands showing that they don't mind if you customize your own experience.

There are no public servers, only private ones. If your host doesn't like them that's between you and them. If you're solo then knock yourself out.

Safe as far as your computer goes is another question. Nexus is generally regarded as safe in that regard. I've got Valheim Plus myself, and the Time Mod so the game will pause in the menu.

Safe as far as not messing up your save or conflicting with updates is one step below that and depends on how fast the modders are at getting up to date. Valheim Plus is hugely popular, so I assume the makers of it work hard to keep it running smoothly.

There are risks involved, but not to your Steam account.