Methinks you're gonna' be ok...
Nice Rims!
But you might want to read this
and you can read here about my experience with those Optimo tires I got OEM on my Fiesta.
An original post from a site supporter to help clarify how important this is.
Because, by photographic evidence you supplied - these tires are near their end of useful life - you will have to replace the tires...
Tires? Not so much. These have not much life left on them. They hardly have any Sipe groove left on the shoulder portion of the tire. The Sipes play an important role of traction control and surface contact.
They are there for different performance reasons - mainly of removing and displacing water when you drive - note that the inner tread has lines - but little ability to shove or displace water off to the side. Those side channels help move water from the inner channels. Look closely, those sipes on your tires shoulder sides are not there - they're blocked from draining off water from the inner channels. Sadly - these types of (worn) treads "dam up water" ahead of them as they roll, and force the water to channel thru inner grooves but cannot shove water off the road surface tread contact. These tires will do fine for a light rain at lower speeds - but high speeds and any rain light or heavy - these tires won't do well. And if there is a lot of water to displace from rain or winter melt, as the speed increases - that dam forms a larger and larger wake and the tread itself can float upon that wake of water and lose more and more of tread surface to this water displacement losing friction and hydroplaning is possible making it harder to keep your car on the road.
Their useful life is about gone - I would not use them for winter or monsoon seasons.
If you need help, look on your cars wheel size on the inner Driver Side Door frame - look for that placard...
Hopefully the inner mounting surface - the ones that are on the hub side, are smooth, flat and square.
I have seen some rims that have aged and corrode due to the alloy reacts to the steel and winter salts starting a electrolytic and galvanic reduction process.
How did it happen? By the excessive re-grinding of the mating surface to bare metal.
Seems that every time you bring your car in to the tire shop and they need to take off the tire so they can change them - they refurnish the inner rim to hub hub surface to remove the corrosion and make sure they're flat - but doesn't mean flat as in flat
Square surface - just regrind the mating surface to bare metal so they will mount bare metal to bare metal..
They should be careful with this and as they age - the rims alloys on older rims are prone to become bad - they can get out of round and uneven - then on top of the needed torque to hold them onto the hub to keep out the wobble when you've driven on them, the gaps left behind on the mating surfaces hold the water to acerbate the process. - so you don't want corroded rims - the sides and walls may be in good shape but the real test and truth - is how the hub to rim surface condition is.
The above is for a 5-lug, but 4-bolt is still the same test.