Colour fading strawberry

Very simple: don't store your chocolate in the fridge. The ideal temperature for setting chocolate is 20°C. You can store it at less or more than that, but not too much. Setting in the fridge results in bad chocolate. Remember, when you work with chocolate, exact temperatures are extremely important.

Here a loose translation from a good article on chocolate/couverture coating:

This is the usual case. You only want a temperature difference of 12° to 13° between the chocolate and its environment as well as between the chocolate and the confect interior.

If the interior is colder than the room, the setting will happen "inside out". The cocoa butter film which gives a confect its shine will build on the inside, leaving the outside looking dull.

This is a really good case for some types of confect, but you can't do it with most types of filling (definitely not with strawberries). Cooling from the outside gives you a beautiful shine.

If you want to achieve a good shine, it is possible to put the confects in the fridge for a short time, but only after they have cooled to 20°C at room temperature. Don't let them fall to fridge temperature, take them out at 15°C. The continued cooling from the outside is beneficial.

This shouldn't happen. The temperature difference is too small, and the confect doesn't set quick enough. In this case, cocoa butter pools on the surface and creates a yellowish layer after it hardens.

When you make your confect, you should time the first piece. The setting should need 10 minutes. If it is less, you don't get all the possible shine. If it needs more, it will get grey or whitish yellow.

Generally, no they should be fine. You'd have more of an issue with frozen than fresh. It would take fresh strawberries a long time to release enough moisture to cause any significant amount of sogginess.

The issue you're more likely to run into depending on the size of your strawberries, the density of your Bavarian cream, levelness of your cake, and the weight of your top layer is that they can act like rollers and friction between the two layers will be low. If the cake is tilted wrong, the top layer will just slide right off. I've definitely had it happen - ruined a cake for a charity event :(. Make sure the strawberries are cut into bits - not halves or slices and preferably fold them into the cream to prevent this from happening. All the flavors will still be there, but your cake will be safer.