I don't really understand why you'd be suspicious of cookies from HTML games, it's literally how all of these games save your data. But to each their own. A love route is totally possible! You have to ease your slaves into it. Use the conversation option "explain" to explain to your slaves their chores. If you succeed, she'll be much more motivated to do her job. Once she's reasonably happy and doesn't hate you, try explaining her sexual duties to her. If you can convince her to accept that she must perform sexual acts for you, she'll be much more receptive to your advances. Combine that with a passionate approach in the seduction menu and you can have happy, loving, passionate sex with your slave which raises affection. Repeat that a bunch, and she'll come to love you as a soulmate.
The other two slots are for slaves, yes. You can equip them with weapons and armor, and once you gain access to crystal hills you can send a slave to the gladiator school in the arena which teaches a slave ranged and melee skill if you don't want to train them yourself. The early game grind can be difficult, but following the main quest and doing some bandit hunting should see you earning enough money to get better gear for yourself and hire some better mercs. never be afraid to dismiss your mercs in favor of better ones. Once you get over the initial hump things get much easier as you'll make exponentially more money from the higher tier fights.
You can buy six of the slaves in the game from the Kymanto hall. Three of them are available immediately upon working for the Kymanto Syndicate (which you have to do for the main quest) and the other three are available once you've followed the questline enough to raise your standing with the Syndicate enough to access the second tier slaves. More slaves can be found throughout the world. At least one can be found through just exploring places, and more can be found through sidequests. The gun store sidequest unlocks one for example. Other slaves are a little harder to find depending on playstyle, like the slave that can only be unlocked through attending a specific course at the academy. If you never attend the academy, you'd never find her.
"A good slave for the start" is subjective. Amelia is my go-to, she's a first tier Kymanto slave. She's already relatively broken and sexually experienced, so she's an easy to train first slave to keep as a maid and sex toy or prostitute. Rebecca and Juno can both make serious money in the Arena, while other slaves have other skills that might make them better as an academy tutor or a dancer at the golden dragon. All I can say is experiment, talk to people, and just experience the world. The rest will all fall into place.