You can sometimes cheese through the tournament early in the game due to the semi random matchups you get, but I'd generally recommend putting that off until later in the game, generally around the time you are planning to fight the four main bosses, as the big reward for the tournament itself is opening up an item and character for recruitment, but doing so requires beating one of the game's nastier bosses.

I don't know if you've been doing this or not, but you can change formations in the menu and Khalid grants everyone the Desert Lance formation at the start of the game -- the formation gives a speed boost to the pointman and has them draw additional aggro, which makes it an excellent position to master Counter from. That said, I'd actually recommend removing Counter from Ellen's move list; she can spark it whenever she is physically attacked and hasn't acted yet if it isn't learned or mastered, but you HAVE to select it from her skill list to use it if it IS learned or mastered. This basically means you can use whatever attack you like if you don't have it learned and she can randomly counter with it if she is attacked before she gets her selected action off, but you lose your action for the turn if you know counter and choose to use it but an enemy doesn't attack you or uses a skill that won't trigger it.

There is a workshop in Pidona you can upgrade Khalid's Scimitar in, and its built-in Demi Rune attack can upgrade into the AoE Demi Echo attack if you keep using it against stronger enemies, and it is a contender for the best damage vs. TP cost skill in the game. Windmill is a super useful tech, and even if it is a pain to master there are several fights it'll make a lot easier if you can pass it around.

I don't know if you got skinny or fat Robin -- Skinny Robin's biggest boon is his high starting MP and good selection of wind magic, while Fat Robin starts with the very strong, and notoriously difficult to spark, Screwdriver; both characters are quite good and worth using. The biggest advice I can give for either of them is to grab an Estoc from the town you recruited them in then push for a Meteor Fragment from an early spelunk into Forneus' dungeon to forge the ultimate Epee in Pidona. Both are decent at sparking its built in tech, which is a powerful, low-ish cost AoE attack; the fire dungeon also has the Nightingale rapier in it, which has a built in heal spell they are both decent with too.

That crown next to your SP means all SP requiring skills cost 1 less to use. You earn crowns for specializing in either physical or magical attacks, and some characters have 'invisible' crowns for specific things they specialize in, the ones I recall being the Robins for Epee techs, Water spells for Boston (I believe), and, due to some odd oversight in the original, Earth for Undine.