The Babylonians noticed that the stars change of position nightly worked out to 1/360 of the Sky's rotation.
Except it isn't. It's close to 1/365.25, which they certainly eventually figured out. I think they liked 360 as a rounder number as it's 6 x 60 and 60 divides by 1, 2, 3, 4, 5 or 6. As well as 12 or 10. Counting to 10 or 12 on hands was very common. Newgrange in Ireland is staggeringly probably over 4500 years old and would allowed folk to count that the year was slightly longer than 365 (after four years the alignment would be a day late). The Ancient Babylonians and later Chinese were also excellent astronomers.
The 360 as an approximation of days in the year, according to Georges Ifrah, is only one of several competing and unproven theories. According to him, no-one knows where the 360 comes from.
Pulse rate is irrelevant unless you already have a measure of time and a number system. A minute of time now is quite different from Sumerian and Babylonian minutes of time.
Phalanges (aka finger and toe bones), claws, tails, limbs and tentacles etc are indeed obvious and likely bases for numbers, though here that has given rise to 5, 10, 12, 20 and possibly others as it depends on if joints / knuckles are counted and how it's done. So for realistic aliens you can easily have several historic number systems and one dominant one. One imagination failure in almost ALL TV/Cinema and many SF is that Alien worlds often seem to have a single homogeneous culture /ethnicity now and in the past. To me that's lazy and unrealistic. So I put different languages (or dialects) and ethnic groups (or vestiges of them) on different regions, esp. continents and often skin colouration related to background region of an ethnic group (near Arctic, temperate, tropics, equatorial might give rise to four main variations of appearance, as might plains people vs jungle (Africa has very tall and very short ethnic groups). Humans in reality vary from 4ft (maybe less than 1.2m) to 7ft (certainly over 2m). Perhaps some aliens might vary in height even more.
Also some African tribes (Batutsi?) commonly have 5 fingers and thumb. Aliens might have variable
polydactyly by ethnic group and maybe two common number bases. (It occurs commonly in cats).
When you build something that is only illuminated at a specific time on the Winter solstice, then a year later you know how many days long a year is.
Virtually every planet has an axial tilt and a slightly elliptical orbit. Which ever of those has a larger effect will decide the seasons. Tilt causes seasons to be marked outside tropics. A more Elliptical orbit and little tilt means seasons change even at equator. If the tilt is more significant (probably common), then seasons change little between the tropics and most outside the tropics, more so as you are closer to the poles.
Solstice means "sun standing still". This only appears to happen due to axial tilt, twice a year. It's more obvious on the short day of winter than longer day of summer, so "time keeping" observatories of the ancients were built for the winter solstice.