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You can always check status at calculator provided at income tax website (external link)
Accordingly, you should inform bank about change in residential status immediately and change the type of account (NRO/NRE Account).
Also you have to open account as resident for MF and tax implications will arise at the time of transfer of mutual fund units. Tax rate will depend on type of fund (equity based or debt based) and period of holding.
Mutual funds whose portfolio’s equity exposure exceeds 65% are equity funds.
Equity funds held for 12 months or more are considered as long term, whereas it is 36 months in case of debt funds.
Short term equity funds are taxed at 15% and debt funds are taxed at slab rate.
Long term equity funds are taxed at 10% (if capital gains of exceeds Rs 1 lakh) and debt funds are taxed at 20% after indexation.