If it's worth anything, my roommate's parents called her Ruth when they spoke in Hebrew. But in general, I'm not sure that this is true: I've never heard it called Shabbath.

It is generally true that fricatives are in a sort of complementary distribution with stops, but it's more morphological than phonological (I was taught this, anyhow; I believe it's a semi-remnant from Biblical Hebrew). It's also generally true that fricatives don't occur word-initially, but a lot of Modern Hebrew speakers use them in borrowings from English.

No variety of Modern Hebrew that I have heard does this. Many native Hebrew-speakers have enormous trouble with the interdental fricatives; my mother, for example, still says [tam] for "thumb" and [diz] for "these" after 53 years in the US.

My uncle's sister is ['Ruti] to her friends and [Rut] in formal situations. ([R] is the uvular trill.)

But I am not a native Hebrew speaker. This matter should be considered unsettled until we find one to ask about it.

What about the Hebrew spoken by the old Sephardi? Is it also the case that the th is pronounce "t"? I think they mostly spoke Ladino, but how was the Hebrew when they did speak it?

I'm not a native Hebrew speaker either, but my wife and children all are. Standard Modern Hebrew changes /b/ /k/ and /p/ into [v] [x] and [f] after vowels but leaves /g/ /d/ and /t/ unchanged.

Simon's comment cannot be the whole story. Consider /mda'beret/, "she speaks"; /mdab'rim/, "they speak". Here we have a postvocalic /b/ that is not lenited.

Also consider /kfar/, "village", which shows a lenited /p/ that is not postvocalic. (All occurrences of /f/ in Hebrew are lenited /p/'s.)

The most you can say quickly is that word-initial consonants are never lenited, and word-final ones always are; but the lenition of word-medial consonants is at least partly governed by morphology. There are minimal pairs that differ only in lenition. I may have this example wrong in detail, but it's something like /da'bar/ "he spoke" and /da'var/ "thing, matter, case".

ACW is right: my previous comment wasn't the whole story. I should have said "single /b/ /k/and /p/". When the consonants are doubled, as they are in some verb forms like /mədabberet/ or /mədabbərim/ (as I would transcribe them), there is no lenition, and similarly when they are doubled because of the assimilation of another consonant, e.g. after the definite article: "spoon" is /kaf/ but "the spoon" is /hakkaf/, not /haxaf/.

/kfar/ on the other hand is not a counter example. Two consecutive consonants never occur at the beginning of a word in Hebrew, and here there is a 'mobile schwa' between the /k/ and the /f/, /kəfar/. It's common in modern Hebrew speech to swallow such a schwa, but it still functions as a vowel by causing lenition in a following consonant.

This is *still* not the whole story, but I hope it will do to be going on with.