Moodle 3.10 requires MySQL 5.7 so this needs upgrading on the server.
Support for MySQL 5.6 ends next week so shouldn't be in use for production websites. If you cannot upgrade MySQL then install Moodle 3.9 which will install with MySQL 5.6.
The other two messages – unsupported_db_table_row_format and mysql_full_unicode support – are warnings, you can install without resolving these. However, it's easier to resolve these now than it is to fix them after the site is installed. To configure your database so these warnings don't appear you should follow the steps for full UTF-8 support in the database installation instructions. In short you should:
1. Add the following lines to the [mysqld] section of my.cnf, the MySQL configuration file:
innodb_file_format=Barracuda
innodb_file_per_table=1
innodb_large_prefix=1
2. Restart the MySQL service to pick up this configuration change.
3. Create the Moodle database with the utf8mb4 character set, e.g. if the Moodle database is called "mymoodle":
CREATE DATABASE mymoodle DEFAULT CHARACTER SET utf8mb4 COLLATE utf8mb4_unicode_ci;
If any of the above are managed as part of a hosting service you should ask their support service if there is any difficulty changing these settings. If your hosting service cannot – or will not – help then I recommend you switch to a different hosting service.