Giriyondo is open from 8am - 4pm and is a pleasant border control point. Make sure you are not taking any new unopended expensive goods with you as they may request for duties (you are permitted to take any material reasonably required for a holiday) and you are permitted upto $50 per person in food to take across the border (anything more and you may be required to pay some duties although this is seldom the case).
Your car will be fine - just make sure you have the papers and permission from the rental company to take the vehicle across the border. Remember to buy your Moz 3rd party insurance at Giriyondo or Massingir gates.
Giriyondo to Massingir gate is 70km or around 1 3/4 hrs. It is a dirt road with some short sections requiring slow driving. A sedan can do this main link road although in heavy rain a high clearance vehicle is a lot better.
Limpopo Park has chalets and camping at Massingir gate and also midway at Aguia Pesqueira. AP will require a high clearance vehicle to get to the camp which has lovely views over Massingir dam. Chalets are very well priced at around R370/night for a 2 bed chalet with small kitchen and bathroom. You can get more info from Heloise at email@example.com
or go to the website http://www.limpopopn.gov.mz/
Petrol stations are at Massingir and Chokwe and Xai Xai.
From Massingir to Chokwe is around 1 1/2 hours or 100km - the road is full of potholes but the (very) good news is that the road is busy being resurfaced although this should only be finished later this year sometime.
From Chokwe you can take a left (at the first petrol station) and cross over the Limpopo and head down to the EN1 which I think is around 1 1/2 hours or you can head direct through Chokwe to Macia where you hit the EN1 and take a left to Xai Xai. These roads are narrow with the odd pothole,but OK.
I would only go to Xai Xai if you are planning to spend a couple days or more at the coast where there are plenty of excellent and good priced places to stay
Hope this helps