Should I have separate mutual fund portfolios for multiple goals

There are no hard and fast rules in this. You can have one mutual fund portfolio for all your goals.

For example - you might have some goals which you want to achieve in the 2-3 years, there could be some which are for 10 years and maybe some for 20 years. Accordingly, to achieve your multiple financial goals, first check your risk taking ability and the investment tenure of the respective goals and then select funds from appropriate categories. Please have these funds in one portfolio and review them annually once.

To assess your risk profile, you can try this https://www.advisorkhoj.com/tools-and-calculators/asset-allocation