Are "ed" or " 'd" often not pronounced and understood via context?

"ed" is often just a tap before the next word. It sounds like you accomplished that well in your recording. "With your" sounded right to me also. However, the "ss" in "impressed" has too much of a "z" sound. It needs to completely be an "s" sound.

If I was to write out how I say it, it would look like this: I’m nah (d)impress (d)with your performance. The two d sounds are really soft and get sorta moved onto the beginning of the next word. This happens to native speakers without people even knowing. When we speak we resyllabify without knowing it, even across words.

You definitely sound like you're saying "I'm not impress with your performance". A native speaker definitely makes the 'ed' sound apparent. There is a t/d sound you should be making but, as /uFledgyApplehands says, it will end up more attached to the word with to make a dwith or twith sort of sound.

I just tried saying impressed with and accessed by aloud quickly in full sentences, and if I think about them, I pronounce the d, but if I'm just saying it casually I think I would actually pronounce them without it. I think it is one of those things where we think we are saying it but we really aren't in fast speech. As for jumped, I seem to always lightly pronounce the d (closer to a t sound as the p is also voiceless).

It sounds like "imprez' there, but should be more like "imprest" 🙃

it's almost always pronounced. you might find exceptional cases where it's indistinguishable to omit the sound but in all of your examples, including your recording, it's noticable as a non-native English speaker or at the very least someone with a very distinct dialect or thick accent to me it sounds like a Hispanic accent. specifically i get very strong Tony Montaña vibes from Scarface. "say hello to my li'le frin"

You dont sound quite right. The "ed" in impressed is coming out more like a "z", or an extended "ssss" that kind of blends to a soft kind of "z" at the end. You are correct is that the "ed" at the end of a word is NOT fully spoken as its own syllable: it is NOT usually spoken as, for example, the "id" in the word "hid" or "kid." And, yes, when you pronounce "ed" you should briefly touch the tip of your tongue to the roof of your mouth just behind your front teeth. The result is that MOST OFTEN (but not absolutely always) the trailing "ed" is not pronounced as a syllable whatsoever - but merely as a sound. And that sound is the sound of the trailing "t" in the word "that". Its what I call a "soft t", which is softer than the "t" in "task", or "tall". A soft t is a little more like the t in bat or hat. "impresst". Not "impressz".

i pronounce impressed like imprest, so it's different than impress but it's not a d sound or a separate syllable

When I naturally say any of the examples you gave, my "d" sounds more like a "t." This is very common.

I think it would probably sound like “imprest with” if I spoke it. It’s definitely not the same as omitting the sound entirely (impress with). That would sound odd

Impressed is pronounced im-prest. Accessed is pronounced ak-sest. Jumped is pronounced jumpt. Pronounced is pruh-nownst.

So I realized this. When I say the word impressed as theast word of the sentence, the ed(t) naturally comes out. What I have to do here is to wait for that ed to come out before I say the next word. Mentally I feel like I'm taking a huge pause, but the recording of my own voice says otherwise. Turned out I had to learn to chill out and not rush all the words out.

I think it's often pronounced but it's soft and quick. Reminds me of a time I said "shouldn't've" to a foreign colleague and they heard should've despite it's being drastically different to me. If they know English isn't your first language then they'll speak slower and the solve unstressed sounds will become more obvious. When I'm talking fast, "impressed with" becomes "imPRESS'd'WIT" (wit can be with or even wid it depends on the word after) so I can see why it'd be tough to hear

There is an actual pronounced difference

The d is really understated, but it's there. It's kind of soft.

So I tried this, I said "impressed with" and "impress with" and tried to see a difference.  There is a difference. If I heard someone say it fast, it might prick my ears up, but I'd ultimately ignore it (much like how "clothes" and "close" are different pronounciations for me, but they're close enough that if someone was struggling with the th sound and just said close, I'd usually not notice).  When I say "impressed with", in my UK, southern, relaxed, not-London accent, I'm not over pronouncing the d but I am putting a slight sound on the start of the "with" -  like "impress 'dwith", if that makes sense. 

[US] They are definitely pronounced, but generally as a “t” sound. The extent to which t’s are actually pronounced is somewhat debatable but there is definitely a sound whose absence I would notice.

I can't speak for all people, but I pronounce the quick "d" sound in those circumstances, and I generally hear others do so. It is a fast tap and somewhat subtle, but it's there.

My "With your" sounds like "wi shore" lol