for your question, i donno if you're mixing up but do not mix up MP with Freezing point. Bigger atom with more intramolecular forces, it will probably have higher mp and bp (they are both usually related except like cis-trans etc.)
also yes 2nd largest IE and largest 2nd IE are totally different. I am pretty sure you're asking about largest 2nd IE, since 2nd largest atom would probably not make much sense.
for most of questions asking for 2nd IE, usually answer will be group IA since 1st IE will put it into noble gas configuration of one lower shell and then 2nd IE will be HIGH since they are very stable noble gases, and it'll be hard to take that electron out of that configuration.
and also 2nd IE is always greater than 1st IE