The monk who came to my husband's funeral...

Among the ceremonies of the Jodo Shinshu sect, there are types that cannot be worn by one person.
It's a type of thing that's easier to wear if someone else holds part of the cloth from behind.
Maybe it was that type of mantle.
If that's the case, it's unavoidable to ask someone else to help you put it on.

I'm in the Jodo sect, so I'm not familiar with funerals of the Jodo Shinshu sect, but I feel like it's possible to extend the chanting of sutras if incense burning isn't over.

Maybe he was a novice monk.

Honestly, I can't believe it either. No matter what denomination the Jodo Shinshu sect is, you will be qualified to become a teacher, chief priest, and ceremonial mentor by receiving the degree to become a masuba monk, and learn considerable manners. In the process, you will learn how to wear a kazai and how to do it. As you pointed out, a gojo kesa can be worn by one person, but it is true that at funerals, there are those that show the greatest dignity, such as the Shichijo kesa, that are difficult for one person to wear alone. In particular, a funeral is an important once-in-a-lifetime ceremony. I practice a lot. I belong to the Jokoji school, but I was originally the most major Honganji school. I think everyone will be executed with due diligence and manners. When it comes to chanting sutras, it is common sense that everyone who burns incense adjusts and works until they have finished. Even for a monk, going to work at a funeral is the ultimate source of tension. I'm really nervous when I think about the heartbreaking feelings of the bereaved families.
My sibling left school for the time being, and I was qualified as a chief priest, but I would never attend a funeral alone. There is absolutely a difference between experiencing and learning and actually being able to do it alone. When I think about the mourner's feelings, I can't give up such a young monk. It just so happened that the funeral was set, and the time for cremation was set, and the wake and funeral were inevitably forced to be performed at this time, and the inexperienced monk went blank, and maybe that was the response. I'm really sorry. I apologize. It made me keenly aware that I must always go back to the beginning and face the ceremony with sincerity and sincerity so as not to receive such criticism. I understand from the bottom of my heart the feeling that you are not convinced no matter how many years have passed. I'm sorry.
Jōkōji Yasuaki

There's nothing you can't do on your own, no matter what. However, monks dare to do that with the help of others.
It is an “ascetic practice” that encourages people to do good deeds, and also arouses feelings of gratitude to the monks themselves.

Having the family temple perform a funeral ceremony was the right decision. Even monks who arrange funeral homes must check if the deceased has a family temple. If so, it is natural for monks to refrain from arranging funerals.

In my case, each wake and funeral is 1 hour long. You will be burnt incense in it, so you won't leave your seat prematurely.
However, wake funerals are not for attendees.
Since monks only think about the deceased and execute them, they can't see the movements around them. A wake funeral is a serious match for monks.

I've read your question.
As a monk, I must apologize for not a few questions Nana had questions at the funeral and was not satisfied.
Now, on to your question,

1. Can monks not wear their own costumes (although my impression is that they recognize that a hat is like a monk's uniform)

As the previous monk also answered about this, depending on the type of hat, there are those that can be worn by one person, and those that absolutely require help from other people. The Shichijo robe worn at funerals is the latter one, so you may have seen it.

2. Can the sutras usually continue while incense burning continues
(There weren't that many attendees either)

The chanting of sutras at funerals is determined by the denomination I belong to. Therefore, during a meeting with the funeral home beforehand, you will be asked to check the chanting time during incense burning and the number of attendees, and increase or decrease the number of incense burners used to burn incense. Unless there are hundreds or thousands of attendees, burning incense will end while the sutras are being recited.

3. Is there any difference between having a monk at a temple with ties to do the funeral and not (the person himself is so estranged from the temple that he doesn't even know his own sect. (Isn't the husband's family complacency)

Is there a relationship of trust about this? Many temples of the Jodo Shinshu sect visit the month for the deceased (although this varies depending on the region and circumstances of the temple), and they meet their families face to face every month. Therefore, rather than having someone from a temple who knows no personality or anything come to the temple, I think it works by trying to have a monk who knows even a little bit of sutras recite. Are those who have died more aware of this than on the part of their relatives?

Anyway, as I mentioned at the beginning, the funeral is a place where all attendees, including family members, remember the deceased and shed tears together to express their gratitude to that person, so if the monk who performs the ceremony made even one person feel doubtful or uncomfortable, we must apologize.
However, I hope that the day will come when Nana will work for hearings in the future and be praised for Nembutsu as an opportunity.
Gassho