When you’re buying options, you only pay premium. While for shorting options, you need SPAN + Exposure margin, it is much higher than the premium you pay for buying options as selling options involves unlimited risk. Do check out this article for more information.
Nope. Having positions across different expires doesn’t have any impact on any position. In fact, if you’re holding multiple positions, for example Short Call and Long Call, this can be same expiry or different expiry, since the position is hedged you get margin benefit which reduces your overall margin requirement. You can learn more here: Benefiting from the new margin framework- an example