Il est tard, C’est tard, even Il se fait tard, are all synonyms, and the only difference is the language level (Il se fait tard being the most formal one).

As for your second question, both C’est lundi and On est lundi are correct. Il est lundi is not.

Time of the day and days of the week do not work the same way:

Time of the day:

• Il est tard. On y va ! means that we’d better go as it is late and we are running late. – Il est applies to the time it is now and this is perfectly correct.
• C’est tard. On y va ! sounds strange. Concerning the time of the day C’est is not expected to apply to the time it is now but to the happening of an event at a given time. For example: Il n’arrivera que lundi prochain ? C’est tard ! is fine. And in this last case Il est tard wouldn’t work.
• Similarly, Il est 8 heures is correct and C’est 8 heures is not. But C’est à 8 heures, applied to the happening of an event, is perfectly correct.
• But On y va ? – C’est tard, c’était il y a une heure qu’il fallait y aller ! works though. In this case, c’est applies to the event on y va maintenant and not to the time it is now. This is why it works. On y va ? – Il est tard, c’était il y a une heure qu’il fallait y aller ! would have worked as well: instead of referring to the event on y va maintenant we would be referring to the time it is now. The meaning would be the same.

Days of the week:

• On est lundi and C’est lundi are both correct and mean exactly the same thing: today is Monday.
• Il est lundi is incorrect.
• Concerning the happening of an event, c’est is fine: N’oublie pas qu’il faut se préparer pour cet événement ! Or c’est lundi prochain.

In usual -but not bad- language,you could use both, but in order to be precise it depends if you have knowledge of the time when you say the sentence.

You have time on mind: Il est tard on y va. is a more pragmatic sentence.

You take knowledge of the time at the moment: C’est tard on y va. could be said.

Something is pointed by the “C'” (an object) on this case this is the time.
The correct but a bit more valuable sentence in all case is more Il est tard
But in order to be more pleasant like on a night event ending: C’est tard on y va is more appropriate as I use it.

Il est lundi (aujourd’hui).
C’est lundi (aujourd’hui).
On est lundi (aujourd’hui).

Are really the same, without any language level sort.

As i see it:

• Usual & multi-usages: Il est lundi

–C’est lundi : More used in the north, it depends.

–On est lundi Probably the best to say in the south where the singing accent can be heard.