After doing our math, we figure out that we need to use a combination of DB pass, point-to-point ticket and regional pass within GErmany and one excursion to Prague

For the DB pass, we go first class... while the point-to-point is 2nd class.

Question:
- is reservation needed for the DB first class pass in month of June?
- any particular timing to consider if reservation is needed.

We learned that DB 2nd class pass has less chance of finding seats together for 3 persons,.. + we got luggages + we find to see the passing sceneries.

June is busy and you have 3 people so on routes where you will be carrying luggage (versus a day trip) I would advise making a reservation.

Not sure what you mean by "timing". I reserve seats on the DB Website for the long segments of our train travel and then at the stations when needed for segments where we do not plan ahead. The lines for 1st class customer service are generally short IME.

Long-distance trains in most countries are busiest around weekends and public holidays. Friday afternoon and evening, and Sunday afternoon and evening are when trains are likely be more crowded.
First-class is used more by business travellers (if their employers pay), so is more likely to be full in the morning and evening from Monday to Friday, especially on Monday mornings and Friday evenings.

The populous states (Bayern, etc.) in Germany have their Pentecost school vacations from June 14 to June 25. At the beginning and and of this period, it is very advisable to make train reservations as it is a very busy travel time. If you travel by ICE, ask for a "Ruheabteil" this is a separate 1st class compartment where no cell phoines, etc. are allowed. On my most recent trips, I had the compartment always all to myself and could leave my luggage on the floor, right next to me.

Especially between 7 and 9 in the morning the 1st class on ICEs is often busy with business travellers - it may make sense to reserve.

Otherwise, don't bother.