It would be possible to put a play corner in the first two drawings but not in alternative 2. I would recommend a corner of storage furniture to corral the toys. I am usually a fan of built-ins but not in this case because eventually the kids will outgrow their toys and you won't need that storage there anymore. The built-in exception would be a window seat under one of those windows on the plans. Some of the storage could be cabinets or bookshelves for bins or toys underneath a window seat. I'm not a fan for toy box style storage because they either become a black hole or the kids throw everything out of them looking for what they want and then do't put the rest of it back. As for the kitchen placement, near to the deck would be best in you like to eat outdoors on the deck or entertain on the deck. We entertain a lot and the kitchen is on the other side of the house from the patio. It's a real pain and a big part of my design brief for the architect was for the kitchen to be next to the patio. I even wanted a pass-through window from the kitchen sink to the patio for ease of clean up but unfortunately I wasn't able to work that out.

Regarding the window that faces your neighbor, if you want to take advantage of the natural light you may want to get sheers. The size dining table will depend on how many people you usually have sitting there to eat. My dining table has a leaf in it, in case I need to expand it. I find that very helpful. A round table will be easier to get around than a square or rectangular one. An oval one may be even better. Depends on your needs. A chaise is very pretty, but I don't know how practical it is. I personally like more space to move around in than stuff. You have to consider the amount of space you have to work with. Try to make lighting an important part of your plan. I like a table lamp or wall sconce in each corner at chest height.

We have floating laminate plank that looks like wood, and it's very nice and has worn well.

Although you have a lot of natural light during the day, you need to plan for good kitchen lighting at night. I would put recessed lights in at least the kitchen area, along all the outer areas the the island. Skip island pendents due to your beams, and just use a hanging fixture over your dining table. You can have more ambient light in the living area, with wall sconces built into the storage areas. Add a floor plug so you can have a floor lamp next to the sofa. I don't understand the kitchen at all. Your sink only has one open side, so you're putting dirty and clean dishes in the same place? And the dishwasher seems like it's in the island with the stove? Move the stove to the outer wall so you can have a regular vent, and put the sink in the middle of the island so it's usable. Put the refrigerator on one of the ends of the cabinet run where it's better accessible.