Can a Muggle use magical objects (potion, Time-Turner, etc)?

Potions, yes.

Tom Riddle Sr., a Muggle, is presumed to have taken a love potion given to him by Merope Gaunt, and it worked perfectly well on him just as it would have on a wizard.

‘Can you not think of any measure Merope could have taken to make Tom Riddle forget his Muggle companion, and fall in love with her instead?’

‘The Imperius Curse?’ Harry suggested. ‘Or a love potion?’

‘Very good. Personally, I am inclined to think that she used a love potion. I am sure it would have seemed more romantic to her and I do not think it would have been very difficult, some hot day, when Riddle was riding alone, to persuade him to take a drink of water. In any case, within a few months of the scene we have just witnessed, the village of Little Hangleton enjoyed a tremendous scandal. You can imagine the gossip it caused when the squire’s son ran off with the tramp’s daughter Merope.

_{-- HP and the Half-Blood Prince (extract on Pottermore)}

While it's not certain that she did use a love potion, we can tell from Dumbledore's supposition that love potions must work on Muggles. If they didn't, Dumbledore would know, and would have immediately excluded a love potion as a possibility.

There's also the Ton-Tongue Toffee which the Weasley twins 'accidentally' gave to Dudley Dursley. I'm not sure whether this necessarily involves potions as such - perhaps there could be a charm or jinx embedded in the toffee somehow? - but at any rate, it certainly works on Muggles. (Hat tip to @Valorum for reminding me of this in comments.)

Time-Turners, probably.

I'm not aware of any canon instance of a Muggle using a Time-Turner. However, I'd guess that Time-Turners derive their abilities from magic done on them during their construction rather than by the person using them, so their performance shouldn't depend at all on the magical ability (or lack thereof) of the user.

They can definitely use Portkeys (even without a wizard or witch there).

Accidents have occurred, however; two Muggle dog-walkers found themselves accidentally transported to a Celestina Warbeck concert in 2003, because their dogs had run off with an old trainer on Clapham Common.
Wizarding World, Portkey Article

I'm not sure broomsticks would — in the flying lesson it's clear that they won't even work for some witches and wizards, so a Muggle who doesn't believe the broomstick will fly probably won't get very far.