Hi JB,
1) What traffic profile is refered to when stating the TPS ?
It's a little dated by now, but F5's performance testing methodology is explained in the following document:
http://www.f5.com/reports/f5-performance-report.pdf
And they've provided suggestions for how to conduct your own testing here:
http://devcentral.f5.com/downloads/f5/creating-performance-test-methodology.pdf
2) Can I use keep-alvie option and, if so, what additional configuration is needed?
You can configure serverside keep-alive with a OneConnect profile:
SOL10067 - Tuning the OneConnect feature on the BIG-IP LTM
https://support.f5.com/kb/en-us/solutions/public/10000/000/sol10067.html
3) Can I assume better performance by using keep-alive ?
You would get better performance using keep-alives than without. But I'm not sure what exact method was used to determine the 2000 TPS rating for the 1500 platform.
Aaron