I hold a valid HSMP. Is it possible to submit for EC for myself and
visa for my dependent at the same time to the home office
Yes. In fact, it is encouraged. They prefer to process both applications together. However, note that you do not submit your EC application to the UK, it is processed at your local British High Commission. Note also, note that the old "Entry Clearance" process has been absorbed into the new Tier 1 system. As such, you will apply for a Tier 1 visa using your HSMP letter as evidence that you are entitled to it. In practise, this is not significantly different from the old Entry Clearance process. See the web site of your local British High Commission for forms and instructions as to how to do this.
I plan to reach UK along with my spouse and find a job later etc. I have been maintaining 2800 GBP for more than 3 months in my bank account for myself and 1600 for my dependent for less than a month.
Is it acceptable?
No. The guidance notes and policy documents all clearly state that the dependent must have held the 1600GBP for 3 months prior to making his/her application.
Also I plan to initially stay with relatives in UK. Do I need proof of this- invite letter from them etc.
Different British High Commission offices appear to handle the accomodation issue differently. The evidence required will very likely depend where you are applying from.
