What are the names of the two phonetic changes in this sentence?

I'm going to be teaching English to French high school students for another year in September, and they all have a hard time with my variety of English (they're used to hearing British English). Specifically, they have trouble with my pronunciation of /t/, vowel sounds, and my merging of words when speaking at a normal pace. I want to be more aware of these phonetic 'phenomenon' so that I can explain them to the students to help them better understand me.

An example sentence that demonstrates all three phonetic issues:

Insert it into the computer.

The "standard" phonetic transcription for this sentence in American English is:

Insert it into the computer.

/ɪnˈsɜrt ɪt ˈɪntu ðə kəmˈpjutər/

I'm from Michigan, and we have a tendency to replace /t/ with /d/, schwa-ify a ton of vowels, and eliminate spacing between words. So I would pronounce the above as:

Insert it into the computer.

[ɪnˈsɜrdɪdɪndəðə kəmˈpjutər]

The first change is /t/ to /d/ - this I know is called flapping, specifically the flapped /t/. So I'm really just curious about the second two: replacing vowels with /ə/, and the elimination of spacing between words (liaison-ification of words?).

As far as my phonology education goes, /ə/ is the most common vowel sound in English, so it's not surprising that I tend to replace vowels with it. But I'm not sure if there is a proper phonologic term to describe that process. As for eliminating spacing/making liaisons between words, I have no idea what that would be called.

What are the names of the other two phonetic changes in the above sentence?

Changing vowels to schwas is called vowel reduction, and it's incredibly common for most English speakers (not just people from Michigan).

Running the words together is called connected speech (not very technical-sounding!), which is also a feature of most English dialects.

As a fellow Michigan native, I will add that one other thing to be aware of in your example sentence, related to the flapped /t/, is consonant cluster reduction. Specifically, speakers in the Great Lakes area often reduce inter-syllabic /nt/ to just /n/ when it's followed by a schwa. So "into" becomes /ˈɪnə/, "interstate" becomes /ɪnərsteɪt/, etc. Some individuals do this much more than others, so it's just something to watch for in your own speech. For example, I'm pretty sure I say /ɪntrested/, not /ɪnər(e)stəd/, but I definitely say /ˈɪnə/ when speaking casually rather than /ˈɪntu/ or even /ˈɪndə/—but I wasn't aware of any of this until a friend from Ohio pointed it out (he does it even more than I do).