Your First Question:
Which schools of thought allow/disallow it?(from the 4 major ones)
The four schools: Hanafi, Maliki, Shafi'i, and Hanbali, allow Katb-Al-Kitab (marriage contract) as a must rather than an optional choice. Allah Almighty described it as a solemn covenant in Surah Al-Nisa (4) — Verse 20 and 21:
In Arabic (the exact wording):
(20) وَإِنْ أَرَدتُّمُ اسْتِبْدَالَ زَوْجٍ مَّكَانَ زَوْجٍ وَآتَيْتُمْ إِحْدَاهُنَّ قِنطَارًا فَلَا تَأْخُذُوا مِنْهُ شَيْئًا أَتَأْخُذُونَهُ بُهْتَانًا وَإِثْمًا مُّبِينًا
(وَكَيْفَ تَأْخُذُونَهُ وَقَدْ أَفْضَىٰ بَعْضُكُمْ إِلَىٰ بَعْضٍ وَأَخَذْنَ مِنكُم مِّيثَاقًا غَلِيظًا (21
In English (in what it means):
But if you want to replace one wife with another and you have given one of them a great amount [in gifts], do not take [back] from it anything. Would you take it in injustice and manifest sin?
And how could you take it while you have gone in unto each other and they have taken from you a solemn covenant?
But there are some minor differences between the schools about the marriage contract conditions and main parts of its validity.
Your Second Question:
Is there a time limit from the point of contract start till the consummation?
There isn't (as far as I know, and according to my research) a fixed maximum limit for its period. However, in the Middle East (which is an Islamic community) the minimum limit would be more or less than a month, and the maximum limit would be more or less than a year. Most people prefer to set it to six months as to not be too short or too long but in moderate. And so to give the couples enough time to get to know each other with avoiding intimacy acts that even if they are permitted in Islam, they are not totally approved among people.
Your Third Question:
For the consummation, does the couple have to stipulate a timeframe (for example: I will consummate after 2 years)? or does the couple have to stipulate a condition (for example: I will consummate once I get a job and can take care of her) or either is allowed?
Yes, this kind of conditions is allowed and common in Islamic communities, but even if both sides (the husband's family and the wife's family) agreed for the marriage to announced publicity after the groom is fully ready for example, a maximum time limit would be demanded so to preserve the virtue and honor of the wife.
Your Fourth Question:
Do all the intimate acts that will be carried before the consummation need to be specified during the time of contract? (example of such acts are: "the couple is allowed to kiss only and hold hands and nothing else" or "the couple is allowed to perform any physical intimacy just without intercourse")
Actually no. Although those acts are permitted in Islam, there is no one is allowed to make them unpermitted especially during the contract procedure. The Sheikh, who would be in charge of doing the authentication of the marriage, will (and should) refuse to write any condition from any side that would contradict an Islamic condition/rule.
References (they are all written in Arabic):
The four schools view about this matter. Here
The opinions of an Islamic community about the duration of the marriage contract. Here
Some issues that may arise in marriage contracts period. Here