The F pronunciation is a regional thing. It's not a pronunciation that is used by most English-speakers. I know that people with thick New York accents and other accents, sometimes use that F pronunciation, but it's not the way most English speakers say it. That's not to say that it's incorrect, it's just that there are a variety of ways in which English is pronounced and they're all acceptable, as long as people are spelling correctly. English has a variety of ways of pronouncing and saying things, like the Jamaican way, the British way, the Scottish way, the Australian way, etc.
Most Americans and English speakers don't say the F pronunciation for the TH at any time.
The D pronunciation is also a regional thing, depending on the accent. Some people, the TH like D's like "Dat" or "Dere..." Some people say it like that, some don't. Again that variation is allowed.
I always say it as "th," I think. Although sometimes the TH is more teethy than at other times. Like when I say "the blanket," the "TH" is quieter, while when I say "the elephant," the "TH" sound is more teethy, my tongue is more on my teeth.
The "TH" is a sound that's hard to explain how to do. You put your tongue against your teeth and blow air through your tongue. You just have to hear it.
---
Actually I should correct myself, you could say "thuh" all the time if you want, but I use the "thee" pronunciation before a vowel along with the "thuh." That's just how my accent is. In English there are numerous acceptable ways of pronouncing things, depending on how you speak and what country you're from and what region you're from. As long as you spell it correctly, and it's understandable. There are some pronunciations, that are always wrong, however. I guess the rule is, as long as enough people say it a certain way, then it's okay.