Bismillah. Alhamdulillahi rabbil-'alamin. Was-Salatu was-Salam 'ala Ashraful Anbiya Sayyidina Muhammad wa 'ala 'Alihi Muhammad.
Is it necessary that I offer taraweeh daily or can few nights be skipped during the month(due to tiredness or any reason other than monthly cycle)? (I take it that you are thinking it is obligatory and afraid of sinning by missing it)
Taraweeh prayer is not an obligatory prayer. Taraweeh according to Sunni jurisprudence is a recommended prayer offered in the nights of the month of Ramadan.
Source - Is Tarawih Compulsory?
Do we have to offer tahajjud prayers seperately?
Taraweeh and Tahajjud are diffirent prayers. So they are not prayed together.
Taraweeh is prayed in Shahri Ramadan, right after Isha Salah in Sunni traditions.
Whereas Tahajjud is prayed everyday during the whole year after midnight sleep, before Fajr starts.