1.This is an area that INS does not make clear. Based on AC21 memo, H-1 transfer is no problem if the gap is less than two months and new H-1 is filed from a legal status (before the date of expiration of the period of stay authorized by the Attorney General). AOS is a legal staus but the problem is that GAP is three months. You have three options. 1. Negotiate a early start date with your next employer, a month early will be fine. 2. File one month after the current H-1 is expired and let CIS decide, 3. File at the end of your current H-1 and let CIS decide. Answer yes to the 485 question and attach a receipt of 485 with the application. If the lower portion (i-94) comes with the apporval notice, you are fine. Otherwise, the I-94 is missing, you need to leave the country to grab the H1.
2. Generally, leaving the country for a few months won't hurt your 140 and 485. Monitoring the online status and ask you friend to take care of your mail. In case a RFE, forward to you. If you have a lawyer, ask your lawyer to notify you any correspances from CIS.