I get a lot of questions from readers, and most of the time, the answers are fairly short. When I feel the question or the reply would be valuable to others as well, I make a post with a collection of them and post them in one go. Today is one of those posts.

"Do you know of any invocations or hymns to Amphitrite?"

No, sorry. As far as I am aware there have either been none made or none have survived. The one quote I like to use when I honour Her is a bit younger, from the 4th century AD. It was written down by Quintus Smyrnaeus, in his 'Fall of Troy':

'A ruining storm maddens along the wide gulfs of the deep, and moans Amphitrite with her anguished waves which sweep from every hand, uptowering like precipiced mountains, while the bitter squall, ceaselessly veering, shrieks across the sea.' [8.62]

This could be adapted to:

'A ruining storm maddens along the wide gulfs of the deep, and [thus] moans Amphitrite with her anguished waves which sweep from every hand, uptowering like precipiced mountains, while the bitter squall, ceaselessly veering, shrieks across the sea. Blessed Goddess Amphitrite...'
"As someone who lives in a very large apartment complex that can't very well go outside and dig a pit in the ground without causing a stir with their neighbours and landlord, what is the best way to properly sacrifice to cthonic deities?"
A pot. I'm serious. Most likely your best bet except for going out and practicing 'in the wild' is to use a standard pot you would put a garden plant in. One you'd put on your balcony, for example. Fill it with soil and maybe some weeds that will survive being dug up every once in a while and getting doused in wine. Is it ideal? Is it exactly Recon? No, but what matters is that you get to dig a (tiny) hole, that you can bury the sacrifice. That it's covered up and gone. Perhaps, once a month (at the Deipnon, for example), smuggle the dirt out somehow and fill the pot anew to start the month cleansed and renewed. That would be my advice.
"I was going through and reading some of your answers to other's questions, and you mentioned that people who want to practice hellenismos need to understand that the theoi come as a one package deal. As a beginner, is it acceptable to start slow and work on introducing yourself to the gods sort of one at a time so as not to get particularly overwhelmed? or is it more like a jump in head first and good luck sort of deal?"
It's the mindset that matters, really. How you go about it is up to you. Say I am just starting out and I want to make a ritual that honours Apollon. What I am trying to convey to people is that when you sit down and you have written down to libate to Apollon and have picked out a hymn to Him, you then think 'how else can I honour Apollon' and make the mental jump to: 'I should include hymns to the Gods who matter most to Him!'. And you'd include a hymn and libation to His sister Artemis, and His mother Leto, and His father Zeus. And depending on the festival, you might include a sacrifice to one or more of His lovers or another God that works within the same domain as the side of Apollon you wish to honour. Asklēpiós, for example, for healing. Or Dionysos in His role as Lightbringer.
What I am trying to convey is that all the Gods are connected in some way and sacrificing to the Gods in the periphery of the main God you wish to worship establishes kharis and is simply good form. I'm not asking you to jump in and celebrate every festival, sacrifice twice daily, and build a dozen shrines overnight. Some never do any of that and that is quite alright. Because, as you have just seen, you will honour all Gods in some way through the handful of rituals you do perform. It's the mindset of it I am trying to get across, not the practicality of it. I hope this explains it!
"How does one apologize to the gods? Like, I used to be a huge believer in them when I was younger, and as I got older I stopped believing. But know I'm starting to believe in them again , and I just want to say sorry for not believing and saying rude things about them but I just don't know how to apologize. Is there a certain ritual or?"
At the risk of alienating anyone--I don't believe you have to. I also don't believe you have to introduce yourself to the Theoi when you start worshipping Them or do anything but give sacrifice, perform rites, and believe. If you had angered The Gods, you would have known beyond the shadow of a doubt. We are talking about the beings who level cities out of scorn and murder every single child of a mother who has shown Them disrespect. I am not saying the Theoi would ruin your life, or that They are vengeful, but I am saying that you would have noticed.
You did nothing wrong by not believing. We are not in ancient Hellas where you would have been raised with faith in the Theoi and you had a rebel period where you decided to raise your middle finger to the sky and every priest you saw pass, shouting at the top of your lungs the Theoi are imaginary. What happened is that you live in a society that--as a whole--does not believe in the ancient Hellenic Gods. You live in a society that has relegated the Theoi to the realm of fantasy and fairytale. You may have said things that you now consider rude--and perhaps they were--but you have since come to realize the Theoi are quite real, and worthy of honouring.
So honour Them. Words are cheap. I believe that the best way to make up for past mistakes is to stop making them in the future. So speak only good things of the Theoi (or at least truthful), show respect and honour, perform the rites, learn of Them and Their lives, and practice the ethical rules They have imparted on us. You don't need a ritual, you need a lifestyle--a faith--and to start living it. The past is in the past, I fear, so look ahead and find the very best ways to honour the Theoi.