1. They will receive an H1B Receipt within a week after the H1B is received by USCIS
2. You may begin working with the new employer as soon as they receive an H1B Receipt Notice under AC21, H1B Portability Regulations. You do not have to wait for the approval.
Keep one thing in mind - Even if you join the new employer while it is pending, there is a chance that the H1B may be denied for several reasons. Especially with IT Consulting Companies, where you will provide services to a third-party Client. If you will work with a Direct Employer, you should be good. Based on the information provides by you, I am assuming that this is a full-time position with a Direct Employer.
3. The time frame for H1B normal processing is 3-8 Months.
Forms Preparation fee for H1B (Extension/Transfer, Amendment) is $295.00 (includes Public Access file), H1B/I-140 RFE write-up Starts at $195.00, H4 EAD $95.00 and PERM/I-140 starts at $500.00, check us out at www.vesaservices.com or email at firstname.lastname@example.org