I went to an interview on tuesday and the employer said he would let me know by next week, but I ask him can I know by friday because I have an offer from another company pending (he know about I got an offer as 'position B' in another company, just that it isn't the position/role i wanted), then he said ok he will let me know on friday.

So yesterday I waited whole day and didn't receive any email from him, so I emailed and ask him instead. He ask if he could let me know on monday, then I said cannot because of same reason. So he said he would have to let me go then.

The scenario is like this, This employer really like me for this particular position A, but currently position A is fulled but he has an upcoming project but only starts on April, which mean he doesn't need me in position A until April. But, because of my past employment experience as position B, he want to put me in position B first until April and I don't mind. But now his position B also really full. 

My question is,
1) Actually is it okay to let them know we have other offer or which other company we went for interview?
2) When he asked can he let me know on monday, does it really make any different if I didn't push him but wait for his answer on monday instead? but tuesday until friday already 4 days...
3) I told him I can start work on the beginning of Jan, should I ask him if I wait another month will he hire me? meaning start work on february.. wil I sound too desperate? will he think I lied to him about another other offer? (but actually I did not lie)

Please advice, I really want this job and this company