1) Not sure if this will change in the future, but you ARE allowed to apply to more than one nursing program at a time. If you are admitted to more than one program, the nursing department requests that you notify them of any offers you will not be accepting so that those "slots" can be offered to another student.
2) As of now, admission is to the NVCC nursing program is no longer on a first-come, first-served basis; it's entirely merit-based (with preference given to Virginia in-state students) and competitive, since only a certain number of slots are available each year. As long as you submit your application requirements before the deadline, you will be evaluated equally among all candidates.
3) Only admitted nursing students can take nursing courses. However, I highly recommend completing any or all nursing co-requisites before beginning the program. These include non-nursing courses like PSY 202, HLT 141, etc. Seriously--having any of these done beforehand will make your life so much easier.
4) That depends. Sometimes the nursing department offers an accelerated in-person nursing program, which includes a full-time summer semester. The other one is the (accelerated) online-hybrid program, which also includes a full-time summer semester. It may be that the poster is using the term interchangeably, or that he/she is specifically referencing one of the programs.
Hope this helps, and good luck with your application!