You have to have the axle fully in the fork ends or properly in the drop outs for anything you want to consider safe to ride. You also what to have a clearance between the tire are whatever part of your bike it comes the closest to. Wheels and frames can flex. So when you are doing something that makes them flex you don't want the wheel to suddenly jam even if it is only the briefest of moments. What that clearance is can be variable depending on the ride conditions and load on the bike. Most like 4 mm to 6 mm minimum or just about a 1/4 inch.
The title of the tire you bought is not an exact tire size. You need to look on the tire and find the actual width. Look for a number that is embossed or stamped in the sidewall, something like 40-622 or maybe 700 x 40 or some other numbers in that format. The smaller number will be the width of the tire and then you can maybe guesstimate what smaller size you should get to try. The height of the tire will get smaller with the width.