Time needed in Beppu

Can I know how much time do I need in Beppu for a day trip from Hakata?

I would like to view some of the hot springs (what bus to take?) as well as soak myself in at least one hot spring. If time permits, i would like to do the sand bath too.

I might want to do a early lunch there as well as a tea break there.

So how much time do I need to do above?

JR Kyushu Pass:
Can I make reservation a few hours before my train or is this strictly at least one day before travelling? What happens if I miss my train after reservation?

Thanks

Can I know how much time do I need in Beppu for a day trip from Hakata?

If you see just a few of the hells, you can do that in 1-4 hours depending on how many hells you visit and depending on your travel pace. Seeing all of them would require more time.

A hot spring bath experience typically takes about an hour, but again this can vary greatly between individuals.

Then I would add two hours for getting around, resulting in a total of 4-8 hours.

The sand bath experience would add another hour, assuming that there are no waiting times (sometimes it can be busy). Lunch another hour.

I would like to view some of the hot springs (what bus to take?)

Access to the hells is explained here:
http://www.japan-guide.com/e/e4702.html

General Beppu orientation:
http://www.japan-guide.com/e/e4705.html

JR Kyushu Pass:
Can I make reservation a few hours before my train or is this strictly at least one day before travelling?

You can make reservations until a few minutes before the departure of the trains, assuming that there are vacancies.

What happens if I miss my train after reservation?

A seat on the train will remain vacant, possibly causing inconvenience to the train company and other travelers. You yourself could make another reservation for a later train or ride any train in the non-reserved section.

You can use this map for find a bath to soak in in Beppu:
http://onsenmeijin.com/map

There are many onsen near the baths, which may be convenient for you.