Partner puts dog and drinking above me.

Hi ladies!
I want to get some unbiased opinions on my situation.
I have been with my partner for 10 months now. Prior to him I was single for a few years after a long marriage. So he is really my second serious relationship.
There are a few issues and some I can live with but some are bothering me, and I don’t know if I’m being unreasonable. He is a good man, and I know he loves me a lot, but I just question whether he is the man for me. We don’t live together but we are together everyday and stay at mine or his every night.
The first issue we started to have was how much he drinks. He knows he has a problem and does talk about cutting back, and is capable of doing it for a little while but then he gets back into the habit of it, recently he has started going out saying he’ll be back shortly and then be gone for hours. He doesn’t lie to me when he gets home, but he’ll spend hours at the pub on the pokies This is something he knows isn’t great and he wants to stop. Of course actions speak louder than words.
Issue # 2 - His dog. I love her, she’s a beautiful dog. But he is obsessed with her. We can’t go anywhere without her, she is always in the car, she sleeps in the bed - in fact she has heaps more room than I do. In my marriage I was never number 1 in my ex’s life, I have never experienced being that important to someone. Now it seems the same thing in this relationship, his dog is definitely more important than me. He is so affectionate with her and tells her how much he loves her and how beautiful she is. And I just sit there watching and wishing he would be like that with me. I have spoken to him about it before, as well as saying I wanted more affection, but things don’t really change too much. He is not callous or mean about it, like I said, he is a good guy.
Issue # 3 - Lack of sex. We are now at the point where we have sex maybe every 4-6 weeks. I can’t handle it, I need more. I spoke to him about it and asked if he found me attractive because I feel very unattractive when he doesn’t want to sleep with me, and he said he doesn’t want me to feel like that. I told him I want more sex. Not a lot changed to be honest. He tried to show more affection for a bit but the sex is still every 4-6 weeks. He did say that it is normal for him to go through stages of wanting it all the time and then not wanting it for ages. I should also point out that I take care of his needs on average twice a week with nothing in return, sometimes he says he wanted to but he finished too quickly, other times he just goes on his merry way. I know that in the past he has paid for sex, so I do feel like shit knowing that he has paid for it but won’t even have sex with me. It just makes me feel really unattractive. And I know I don’t want a relationship with no sex. We should still be in the honeymoon phase but it’s like we rushed into a 20 year marriage type relationship.
The difficulty is that I struggle to talk to him about the sex thing because of how I was brought up - we don’t talk about sex. Now I am trying really hard to break that behaviour but it’s not easy. I also struggle big time with putting myself first, I will always put others and their needs above mine. I know I need to change that a little but there is a lot of history as to why that is very hard to change.
I do really love him, and I do want a life with him. We have talked about marriage and babies etc. So it’s hard to just throw it all away when he is a good guy and I do adore him. I know that I should talk to him about it more but I guess after the first couple of times I tried that I’ve just kinda shut down a bit. After my unhappy marriage I swore I wouldn’t live like that again and I’m scared that I will regret staying with him.
What would you do?