Doesn't all fighter type characters including Paladins have the option of choosing the Weapon Specialization feat ? It appears the games pre-generated Paladin character (Alhandra) is not allowed this feat after she attains 5 level. Or is this a bug in the game ?

Weapon specialisation requires 4 levels in the Fighter class (and the relevant Weapon Focus feat). Levels in other classes don't count. (with the exception of some prestige classes like Eldritch Knight which explicitly state they do)

So a Paladin that already has Weapon Focus for Longsword should have the option of Weapon Specialization for Longsword when it reached 5th lvl......correct ?

No, a character needs both the weapon focus and at least 4 levels in the Fighter class to take Weapon Specialisation. Paladin levels don't count.

(The Fighter, Paladin and Ranger classes are sometimes lumped together as Warrior classes, but they're not the same.)

Thank You for the clarification. What feats would YOU use to make your Paladin powerful ?

To be honest, I wouldn't add a Paladin to my party in ToEE. I consider them to be bad Fighters with a few special abilities that aren't all that spectacular and the spells come too late are too few to be of much use.

If you picked the default Paladin and started with dex 8 then a lot of good option become unavailable (like combat reflexes while using a reach weapon) I suppose you could pick power attack and cleave. Shield based stuff is not very useful because your AC will always be low thanks to dex 8.
If you rolled your own Paladin, you could go for reach weapons of maybe shield based feats.

Paladins don't get Weapon Specialization in TOEE? OMG