Yes the molecules are being pulled apart due to the stronger gravity closer to the black hole. Space-time stretching may have some effect in the last millionth of a second before the object is pulled in, but the object will already have been spaghettified before that happens.

Here’s a bit of math to back that up:

a=G*M/r2

Acceleration = gravitational constant * mass / radius(distance to mass center) squared

G=6.7e-11

Earth check:

M= 6e24

r=6378000m=6.4e6m

a= 6.7e-11 * 6e24 / 6.4e6^2 = 9.8m/s^2

3 solar mass black hole:

M= 6e30

r_feet = 1000000m (your feet at 1000km away)

r_head= 1000002m (your head)

a_feet = 402,000,000 m/s^2

a_head = 401,998,392 m/s^2

Looks almost the same but your feet are being pulled away from your head at 1608m/s^2 , or 164x Earth gravity! You’re also going close to speed of light and have only a few milliseconds left to live.

Above is Newtonian math and is good enough to answer your question. Even if you’re going 99% the speed of light, spacetime dilation is only 14%:

γ = √(1 - v²/c²) — Lorentz factor

= √(1 - 0.99²) = 14%

Not noticeably faster, but yes it’s possible that other planets may experience time a bit slower than us. Time slows down with lots of mass nearby (this is what causes gravity). So if another planet was orbiting near a neutron star, it’s time would go slightly slower relative to our point of view.
There is also relativity, where if the planet is moving away/towards us very fast, its time will be relatively slower. For the real mind trip, we’d also be going slower from their point of view! There will be planets out there whose time goes eg 0.000000000000001% faster than us, because they have less nearby mass.