My partner does not meditate with me. Yet! I started my journey for myself because I needed to return to me and grow my inner joy. I talk to my partner though about the fact I began this journey, how much better I feel now that I have meditation in my life, I ask if my partner is interested in meditation at all, and I have asked my partner to meditate with me! I think for my partner it is important to observe first as it is new and strange to them presently. But the more I change and grow positively and my partner can see it and I continue to gently ask my partner I believe they will join me in the future!
That being said, I believe the awkwardness you may feel will fade as you practice more and feel the benefits yourself. You will want your partner to feel good also. But maybe your partner got you to meditate and to start the Fabulous so maybe just let your partner know how it still makes you nervous being new to it and once you are more acclimated to the process then you will be ready to share this special time.
I believe meditation is always for your inner you; however sharing the energy of it all in the same room can be beneficial to each individual in the group! The key is showing respect to your partner or friend making a safe understanding space for all.
2. They don't join. They could, but I don't force it on them. Everyone has their night time rituals. I have avoided doing my seated meditation in front of them because I felt silly. However that is a completely me issue as they don't care and would never say anything negative about me trying to be healthier. I do meditation in bed with them reading there beside me. We have a Google Play mini and it is connected to headspace, it has sleep and general meditations seemingly for free since I don't pay for that. Listen to the sleep one fall asleep while they read. Not awkward at all. It's kind of nice. My goal is to do my kneeling practice in our bedroom without feeling awkward. I'll do it the next time. It's easier though to not feel awkward because they know about the benefits of meditation, and my relationship this time around has been based in mutual respect and support. If your partner has said anything to you that is demeaning or hurtful they are not someone I would want to be with. Supporting your practice is super simple of they can't do that how will they support anything else you do? ALSO when I am at my parents they know I'm meditating 1) by seeing me on my mat and 2) by hearing my guided meditations. The challenge here for me is that they're usually calling my name until they come up and realize. I don't break and speak when I'm practicing.