This is not a problem. You will probably be parking along [35] in one of the many available areas. The geothermal park with Strokkur is a very short walk. It is not necessary to drive on F333. If you do, F333 is paved up to the marked entry area to the geothermal park with Strokkur. Exploring the area in Google Maps in Street View is helpful.

There is a car park next to the Geysar area, yes.

Никак. Дешевле будет взять тур по золотому кольцу (помимо гейзеров еще Тингведлир и Гюдльфосс). Или машину напрокат

No sé si hay visitas guiadas en español, pero no sé necesita entrada para ver el geyser. Es posible que por la noche y por precaución la zona la cierren porque sí había una pequeña valla, pero el horario creo recordar que era muy amplio.

Elodie, l'entrée du Geysir n'est pas payante. Gullfoss est très facil de visiter, pas loin de Geysir (en voiture, bien sûr). Pas besoin de passer par une agence.

Free! Even Free parking (correct at writing March 2018)

Hi, Strokkur is the geysir. It's also close to Gullfoss Falls (10-15 min drive). We stayed at the geysir hotel which is right across the road. Hope that helps!

No entrance fees to see Strokkur. There is a car park across the road which offers free parking. There are several cafes / restaurants / gift shops nearby where you can purchase food and gifts as you wish.

Hi, because your time is very limited on the way there and back, I would recommend either hiring a car yourself from the airport and driving (try Blue Car Hire - they are outstanding), or using a private transport company who can tailor a tour to suit your time. They can pick you up from the airport and drop you back too. There are quite a few private tour companies listed on Tripadvisor who are affordable and once you provide your time details they can tell you what they can fit in for you. I doubt you'll be able to do the National Park as there is so much to see here, however Gullfoss waterfall and Geysir is doable. If you end up hiring a car, make sure you request a GPS as this will make things easier for you and lessen time wasted. As for the Blue Lagoon, make sure you book ahead or you'll miss out altogether. They receive dozens of coaches and buses all day long and entry is timed, so it's busy all year round. An alternative is to book a bus tour from the airport to take you if you plan to do nothing else that day but the Blue Lagoon. Have a lovely time in Iceland.