regarding your inquiries
1) If it is Visit Visa or Business Visit, the duration of the visa is within 1 month only. Make sure the the ticket they provide is a two way ticket (computed from date of entry until 1 month, that corresponds to your visa, so that in the airport verification there will be no problem with the immigration)
2) After 3 months they sign, because you have to undergo series of test, X-ray, blood group, blood test. (But make it clear my dear because there are new rules here in Qatar that Visit visa to be converted in Working Visa must be processed as soon as possible within that 1st month of entry or else you go to jail.)
3) In signing your contract these are the hints. Make sure that the company who sponsors you are the one's stated in the contract ex. 1st Party Company, 2nd Party Employee "You". Qatar Labour Law 14 2004 article 38-39
4) Make sure that your basic salary and the date of your salary is stated because there is a lack of specific date of salary article 65-66 of the same law.

Please try to read this okay,
I hope it can help you.
http://www.qatarliving.com/files/LABOUR%20LAW%20STATE%20OF%20QATAR.pdf