HOME LOAN WITH LONG TERM

Is it fine to apply for a home loan with a longer term to get low EMI and then do part pre-payment with existing funds? Or, should one apply for a short duration loan instead?
The basis of choosing the home loan tenure is based on your income and age of retirement. If loan eligibility is a constraint, go for the longest possible tenure (some banks allow 25 years though most banks allow only up to 20 years). The maximum tenure is also restricted by your age at the end of the tenure. In case you are self-employed, the age of retirement assumed by most banks will be 65 years.

Even if loan eligibility is not a constraint, you should opt for a longer tenure with no prepayment penalty option. This way, you retain the flexibility of low EMIs and prepay the loan whenever you have surplus funds.
As far as partial-prepayments towards the home loan are considered, the decision depends on the availability of surplus funds. Also, please check the loan agreement to know the clauses regarding prepayment. Most banks allow partial-prepayment towards home loan after a certain period of time; without prepayment penalty. This can also reduce your EMI burden.