There are all kinds of babies. My first was not a sleeper either - she took 20 minutes naps, needed my attention all the time and didn't sleep through the night for a long time. My second child took three hour naps and slept through the night at 12 weeks and was content to sit in his bouncy seat and watch me do stuff.
Give yourself permission to have a messy house. Allow yourself some time to just sit and stare out the window. Then get up and do stuff. Put baby in a bouncy seat and carry him around your home as you do stuff. I used to put my daughter in her seat on the kitchen table while I did the dishes - I would have to turn to talk to her - but while I rinsed I'd talk to her. I'd bring her boundy seat in to the bathroom while I took a shower, or while I folded laundry. I ended up doing a lot of things on our bed becuase I could lay her on the bed, leaning against the pillows and sift through papers. Allow your baby to cry when you need 10 minutes to run the vacuum or mop the kitchen floor. Eventually your heart WON'T break when you hear him cry - it's just his way of communicating since he can't talk. He wants your attention and he's learned that when he cries you show up. Let him learn that when nothing's wrong you won't always go to him when he cries. You'll learn the difference between his hungry cry and his tired cry and his "I'm bored come amuse me" cry.
You can connect with your husband when baby's awake - put him in his little seat on the floor and the two of you cuddle up on the couch. Let baby watch old movies with you maybe he'll fall asleep. As for sex, for thousands of years families have lived in one room huts and manged to have more than one child - so parents were under the blankets getting busy while baby slept across the room. At this age they have no clue what you're doing - so don't allow yoruself to stress on that either.
These early months are a tough season to go through - they don't sleep well, you don't sleep well - you feel yucky, you've lost the ability to keep your home neat, and you just want to sit down and cry sometimes. Every mom has been there - so allow yourself a limited period time to "wallow" in the stress, like ten mintues, and then get up, leave it and go on to the next thing. This is a season of your life - it will pass - I promise.
You say that you're overseas - but not sure if you're in an area where you can put the baby in a stroller and go for a walk - that will help tremendously - give you both fresh air get some exercise and release some endorphins into your body. Try to get out there and connect with other moms - there have to be other american moms you can find on google. Maybe you can share babysitting to allow yourself that precious time you so need right now.
Finally pray - God does care about the small details of your life - He didn't create you so you would be frustrated in life. Ask for his direction and discernment and companionship of other moms.
You will get through this season and you'll do great if you allow yourself some grace!