You are specifying criteria that presents numerous challenges to a race developing intelligence, much less science, much less medical science. The primary issue is that, not being a predator, they could not be an apex predator. This means that they would suffer from predation from animals and parasites that they ethically couldn't defend themselves against. It is irrational to think that an ecology could develop without predation and parasites.
The primary obstacle to them developing medical science is that they would be banned from any form of experimentation that might possibly result in harm, even as small as causing rashes. All medical experimentation would be done on volunteers, or it would remain hypothetical.
This is similar to the problem we currently have with string theory. We can theorize all we want, but we have no way to test it. This makes progress nearly impossible. The best we can do is suggest numerous formulas that fit the evidence.
Volunteerism would help this, but your concept of "harm" has to be addressed. Is it harmful to provide people with pain killers? That's an oddity of our culture where we feel that relief of suffering is the same as doing harm, so maybe not. Given your "reverence for the dead" criteria, I suspect that they may think this.
The biggest obstacle is their passive nature. The way you describe them, they try to work with their environment instead of against it. They might consider illness to be just a natural part of the cycle of life. I think that would be their greatest obstacle.
Here are a few areas where these philosophies would also prevent them from becoming the dominant life form on a planet.
All life is sacred. They do not kill unless they must.
This sounds good when presented, but it means that they can't eat. All eating requires killing, whether your killing cows or broccoli or bacteria. Every society draws a line on the "close to us" scale where we no longer consider the creature to be worthy of consideration. For humans, it's usually other humans. If a creature is a house pet, they get included. Vegans include all animals, but happily kill plants and bacteria.
The plant/animal divide is something that's specific to Earth. They might have something similar, so you're going to have to figure out how far back in their ancestry the "don't kill" applies to.
If they're purely vegetarian, this means that they have very inefficient digestive systems. It's really hard to derive calories from eating just plants. We had to advance our agriculture, transportation, tool use, and organization to 1900's level before being a vegetarian was an option that wouldn't kill you. Paleolithic humans would never have survived, much less flourished, if they were restricted to eating plants.
Do no harm. Even if no one dies, doing physical or emotional harm is just as bad.
Now you're telling me that they aren't allowed to hurt each others' feelings. Can you imagine a world where we can't disagree with other people?
Humans are memetic duplication engines. If your alien race is capable of learning then they are, too. We copy things we see, and we innovate from them. This includes clothing styles, culture, tool use, language, etc. When we take these ideas as part of our functional knowledge base, they become part of our identity. This is why Identity Politics is so destructive. You can't tell a person that they're wrong without hurting them because their ideas are a part of who and what they are.
Freedom is precious. They do not keep their pets in cages or pens, much less each other. Literally or metaphorically.
There are a lot of problems with this, but let's combine it with the previous rule. Now you've made it impossible to present logic that boxes people's minds in, forcing them to realize that what they've been doing is horribly, terribly harmful to others. If you creatures never make mistakes, you might be able to get away with this.
Let's combine this with "all life is sacred." If we tried to implement this here, does this mean that we aren't allowed to tell our pets that they can't destroy our stuff? That we can't build houses to keep animals out? Can't put fences around our crops?
The good samaritan law. They are compelled to help those in need.
I think the other answers have adequately covered this one. The failing of communism was its essential tenant: Work to be done by the capable, aid to be provided to the needy. This means that the best strategy is to be the least capable and most needy, causing the collapse of society instead of making a utopia.
Respecting the dead. The only time they touch a corpse is when burying them.
This one is nonsensical. Are they required to either bury every dead animal they find, or leave it to rot? Where do they get all the land required to bury these people and animals? Can you imagine the burial process for an elephant?
Can you plant crops over the corpses, or would that also be abuse? Are mass graves disrespectful? If not, how far apart do the bodies need to be placed?
I spend a lot of my time dealing with the overflow of cats in our city. Cats will expand to consume all resources in an area. There are people who complain that it wouldn't be a problem if everyone loved the kitties, but if they did so, there would just be more cats, and there would still be a feral cat problem. All animal populations will expand to the size of its environment, including consuming all of the love you can give, and they come back for more.