some monsters say "casts bloodlust" or "casts random spell" ect. How do you do this?

In HoMM3 these are automatically cast for you, and usually have a % chance of being cast. It doesn't use their turn, and is simply a bonus.

In HoMM 5 some of your creatures have "abilities" such as Archangel's Resurrect or Griffin's Battle dive. It is also possible in 5 to have some of your creatures cast spells instead of attacking - I think for example Dwarven Runemasters can cast Firewall, and mages can cast fireball (when upgraded).

IIRC (too lazy to check) in HoMM 3, when it's the Ogre Magi's turn just move the mouse cursor over the friendly unit you wish to be the recipient of Bloodlust. Then it will change to the "Cast Spell" symbol, and you can lefy click to cast the spell.

Most of abilities are either automatic (Dragon Fly's Dispell and Weakness, Enchanter's random spell, Mighty Gorgon's Death Stare, Mummy's Curse etc.) or passive (Unicorn's Resistance Aura, Azure Dragon's Fear, etc.), but some of them can be used in a controlled way and they include: Archangel's Resurrect, Ogre Mage's Bloodlust, Master Genie's random beneficial spell, Pit Lord's Demon resurrect, Air/Water/Fire/Earth Elemental's corresponding elemental protection, Faerie Dragon's random attack spell.

Depends on the ability; not all are automatic. The two examples given by trademark are in fact not automatic and have to be cast by moving the cursor over a friendly unit and clicking, which uses up the caster's turn.

Depends on the ability. As indicated, some are automatic (Dragon Fly triggers on attack, Enchanter casts at start of his action), while some need to be triggered by you (Ogre Magi, Fairie Dragon). If you need to direct the creature to cast, then when the creature is active,mouse over a valid target and you should see the icon for casting a spell. Click to cast.

For example, when your ogre magi is ready to take its turn, then mouse over one of your other units that are not immune to fire magic (so not green/red/black/gold dragons or effreet, for example), then click to cast.

Note that you can't direct your creatures to cast spells on themselves, so splitting your Archangels into two (or more) stacks will allow them to resurrect each other.

Be careful with Fairie Dragons! The spell they choose each round is random, so make sure it isn't AOE before you hit an enemy stack that is surrounded by your own stacks. The readied spell will appear in the message log at the bottom of the battle screen.