https://assets.documentcloud.org/documents/6454557/2019-10-04-EEC-Engel-Schiff-to-Mulvaney-WH-Re.pdf
https://www.nbcnews.com/politics/trump-impeachment-inquiry/read-subpoena-house-democrats-sent-white-house-trump-ukraine-documents-n1062766
The so called "five chairs letter" referenced within it:
https://judiciary.house.gov/sites/democrats.judiciary.house.gov/files/documents/FiveChairsLetter8.22.pdf
"Subpoena" sent to Mike Pompeo:
https://oversight.house.gov/sites/democrats.oversight.house.gov/files/documents/2019-09-27.EEC%20Engel%20Schiff%20%20to%20Pompeo-%20State%20re%20Document%20Subpoena.pdf
A sample subpoena legal form for the jurisdiction of The District of Columbia:
https://oah.dc.gov/sites/default/files/dc/sites/oah/publication/attachments/OAH-402-General-Subpoena.pdf
If you read the source material, you will see some very distinct legal terminologies that give a subpoena force of law completely absent from these "subpoenas", which in reality are just carefully worded requests for information. Pelsosi could in theory issue subpoenas from the various sub-councils, but this would be ineffective because until there is a vote to engage in an official impeachment inquiry, the two branches of government stand on equal levels of authority and the president is well within his rights to exercise executive privilege. If the full house were to vote, and it was passed, this protection under executive privilege would be severely limited, however it would also grant the president the authority to issue his own subpoenas.
Pelosi knows this full well, and knows if she does this, Trump is going to take a massive shit all over the Democrat party by exposing all of their own corruption and getting it on public record for everyone to see. As I previously explained, they are boxed in. If they vote to impeach, they give Trump the power to bring his own evidence. If they fail to impeach they piss off their own base. Hence they are engaging in a strategy of PRETENDING to impeach and PRETENDING to issue subpoenas in order to play this out as a political and media battle rather than a legal battle, IE an actual impeachment. This strategy satiates her base, confuses most of the public who don't have the time or inclination to bother to look this close, and creates "bad optics" for Trump, but has ZERO AUTHORITY under law.
Half of the house engaging in "impeachment" is not constitutional nor is it due process. If the accused has no ability to defend themselves and the accuser makes all of the rules, that is not due process. If the accuser ignores all previous precedent and constitutional balance of powers between the branches of government, that is not due process. This is all a made for TV movie, not a legal proceeding, and you all lined up to buy tickets because it serves your confirmation bias. Just don't forget your $15 tub of popcorn rubes.
Some more reference material:
https://www.westernjournal.com/ex-fed-prosecutor-mccarthy-despite-dem-antics-no-impeachment-inquiry-happening/
https://thefederalist.com/2019/10/08/white-house-tells-pelosi-your-fake-impeachment-subpoenas-have-no-real-legal-authority/
https://canadafreepress.com/article/subpoenas-not-valid-since-there-is-no-impeachment-inquiry
https://www.nationalreview.com/2019/10/impeachment-inquiry-house-must-vote-or-its-just-democratic-stunt/
https://www.lucianne.com/2019/10/07/house_sends_more_carefully_wordedbr_impeachment_demand_letters_not_brsubpoenas__omb_and_pentagon_17139.html
https://www.realclearpolitics.com/articles/2019/10/02/pelosis_sidestep_on_impeachment_vote_cuts_both_ways__141391.html
As for issuing his own subpoenas etc, I get the impression it has nothing to do with impeachment, but which committee is doing things. If I was Pelosis I'd probably do the same thing just so he couldn't turn it into a circus and just get it done and then, assuming they want to go through with it, get it into the hands of the senate as soon as possible and let them have their shit show.
I really don't get the whole "real impeachment" thing. Congress can do things how they want. The right just throws out "prior presidential" impeachments as precedent but what about all the other impeachments. The constitution seems pretty crystal clear to me, congress has sole power and can run things however they want. If he gets impeached, then maybe he should try and take it to the supreme court and get a ruling on it or something. If it's such a big deal, then maybe they should have written some laws or do some constitutional amendments to set out exact procedures to follow. But really, do you think either side wants to really do that? They all love the show they get to put on far to much. I must say though, I'm a bit surprised at how little the Dems are making this a show. I thought it would be a hell of a lot more. Almost makes me think they're actually serious about it.
Funny that you would post links to pretty much all right wing sources and then talk about other peoples confirmation bias. I also noted that most of them showed a hell of lot of "red" on newsguard for "This website severely violates basic standards of credibiilty and transparency". I find that humorous since it's not exactly tough to do things in a way to get some green from that tool so the overall rating shows green. Even breitbart shows up as green (despite two categories I would consider very important being red for them)