We removed a counter penninsula in our kitchen. We have laminate flooring, and have enough left over to patch the hole in the floor where the cabinet once was. About a 1 ft X 4 ft area. Is there any way to do this that is easier than taking the entire flooring up, up to that area and then putting it down again. Help please!!.

As long as the tile isn't a wood look, it's fine to mix tile and laminate. However, these days most people tend to prefer a single flooring throughout a home. Laminate is not a good choice for areas that get moisture such as bathrooms, kitchens, and entryways, so if you do want a single flooring use something like engineered hardwood or LVP. If you go for the two flooring materials, make sure that the whole floor will be the same level. In other words, make sure you account for the height of the tile now when putting in the laminate so that you don't create a tripping hazard and think about how you would do handle the transitions. Also, laminate floors tend to go through styles quickly, so I recommend buying some extra in case you need to patch or extend in the future.

I installed commercial rubber tiles in my basement which are likely to be somewhat stiffer than your gym floor tiles. My experience may not be exactly comparable but it is a similar product.  We found that getting the surface suitably smooth to be more challenging than it appeared at first glance. My house is from the 1930s so the basement slab had many divots to fill. After that we had some ridges and valleys to smooth out. We could have chosen to rent the equipment to grind the slab but did not wish to go through that process. Instead we used an angle grinder to knock down the highest spots. Then we used a long straight edge to find the valleys for the first run with a portland cement based feather finish product. After that, we skimmed the entire surface and then used a rough stone to knock down any ridges before the product was completely cured.  I don't know how picky you are and what final results are acceptable. For me, I expected to use the space extensively for many years so I invested considerable time and effort in surface prep. From a distance most slabs look flat but up close the low spots show up. Try mopping the floor and see where the water pools for a quick idea. If you expect to exercise without shoes or do lots of floor work, you will find your body can feel an eighth inch floor dip on a relatively hard surface. High spots aren't as obvious to me but a slight valley seems like a ditch to my stocking feet. If the surface isn't flat, the tiles won't line up evenly and since I had about 600 sq ft of 2x2 tiles, I wanted clean corners and tight seams. We used a skim coat product from Uzin with the first sacks from ReStore. Additional product and the adhesive was purchased from the commercial flooring supplier where we purchased our wood flooring finish. They also sell the comparable products from Ardex. The product is not cheap but each sack covers a large area. Those products set extremely quickly so mix a small amount and be prepared to work fast. The Quikcrete product mentioned before is a good product for larger holes and edges but you may wish to use a finer finish product if you choose to smooth the surface of the slab before gluing the tiles.

Take a look at these samples of Brazilian Cherry peel and stick flooring. I bet you might see the color of your floor. Use that and a rug, it might look original. https://www.google.com/search?client=firefox-b-1-e&q=brazilian+cherry+peel+and+stick+tiles&tbm=isch&source=univ&fir=RF5M1-9UhldgiM%252CL__SUjoUM-j1UM%252C_%253Bemt-llordVMqhM%252CwS4bgq_yJCZQeM%252C_%253BYX3FvHJtv-toRM%252C9oZHIiYiPraoMM%252C_%253BwU7aFHEp6aiC2M%252CDPFRIIVLyfQQbM%252C_%253BOfr0FTeYEzboQM%252C8CUeq58W0cmhUM%252C_%253BpqbDLzUPxQqUjM%252CZQMtvO5wOrSdeM%252C_%253BQk_TO2xxbFeQUM%252C_LWIbJweoQZIwM%252C_%253BnrsooBrW5rFLfM%252C6ieWMZLLn4lwVM%252C_%253B0-c-AD9nRZWWFM%252CtsBpoYBZdqconM%252C_%253BDvyznIeifCBH4M%252CozcsdcKd82K_vM%252C_&usg=AI4_-kQD2Y8LFZpyr2g6yyvJrV8IZ6k0BQ&sa=X&ved=2ahUKEwjS79TUy76AAxVNkokEHXEnDJcQ7Al6BAhHEBM&biw=1280&bih=639&dpr=2