In that second question I'll give a shot. If someone has more experience chime in.

In my experience and reading the IRS instructions the 1099 is for the period you are getting paid by the customer. The CUSTOMER will or should (if your business formation is the type to receive a 1099) send you a 1099 for the payment in the prior year if over $600. The fact you don't get it in your bank isn't something the customer will know if issued close to the end of the year. You will receive the 1099 and that income will go into your tax forms. --- Unless you're on a cash basis. 

In that case I'd guess it would be an explainable difference. If it is large don't forget to make quarterly tax payments fed/state as you see fit. 

https://www.irs.gov/instructions/i1099msc#idm140364727411008