Can I pray al fajar anytime after the sunrises? Can I pray magrib anytime after the sun sets?

You can’t pray Fajr namaz “after” sun rise but yes if you want to pray after the sunrise then your Niyyat will be for Qadha Salat. After the Sunset when the redness has disappeared from the horizon which take around 15 or 20 or even 30 minutes in some areas then it’s Maghrib time now from this time till the mid night you can pray your Maghrib salat.

Also please refer Fadhilat times for each Salat:
The Prime Time/ Awwal e waqt remains almost the same for all the prayers but Waqt e Fazerlat differs.
The estimated time of fadhilah for five daily prayers:
Fajr: From Azan till 21 minutes roughly
Zuhr: From Azan till 1 hr 40 minutes
Asr: Around 2hrs 50 minutes after Azan e Zuhr which lasts for 42 minutes roughly
Maghrib: From Azan till 51 minutes roughly
Isha: After 51 minutes of Azan e Maghrib.
Please note the prime time is the best time for Salah unless anticipating for jamaat and second comes time of fadhilah.

Imam Jafar Sadiq (as) has said:
Verify our true shias with two qualities; observing the timing of Salah and exerting the best financial supports to their brothers and sisters in faith.