Some things to point out:

• Unless you're attuned to the specific cause of a background count (for example, a toxic mage in a radiated super polluted crater), background count is applied as a dice pool penalty; not a bonus. Not all background counts have causes to which you can be attuned; you can only be attuned to aspected background counts. If you're attuned to an aspected background count, instead of applying the bonus to your dice pool, you apply it to your limit.
• Sorcery is the skill group that Spellcasting (the applicable skill) is apart of.
• The drain for the Manaball spell is equal to the Force at which it is cast.
• Direct Mana spells (like Manaball) do not allow for dodge, cover, or visibility modifiers; If you can have Line Of Sight to the target and you cast the spell, they get hit. They resist your Spellcasting roll with Willpower, and however many net hits you get is the amount of damage they take.
• Defenders win all ties unless stated otherwise.

Your spellcasting pool is then 6 (Spellcasting Skill) + Magic - 1 (Background Count) with a limit of 6 (Force), meaning at most you can get 6 hits unless you use reagents or Edge to modify the limit. The target resists with 4 dice (Willpower) and no limit. If you both get the same number of hits, the spell has no effect. The number of net hits you get is the amount of damage the target takes. This cannot be soaked or lowered. Finally, you need to resist 6 points of drain. If you got more hits on your Spellcasting roll (after applying the limit of 6) than you have Magic, the drain is physical. Otherwise it is stun. To figure out what dice to roll to resist drain, check your Magical Tradition. For example, Shamans resist with Willpower + Charisma while Hermetics resist with Willpower + Logic. Since these pools are attributes-only, there is no limit.

If it would be a elemental manipulation we would need to mods to the list above for range and movement? (e.g. +4 points range and -1 target is not moving)?

I don't really understand this question. Manaball is not an elemental spell, and none o the modifiers are applicable.

Would you increase the modificator if the target is small (e.g. a mouse)?

No. Direct spells affect the target as long as you can see them; no matter how large/small, how fast, or how far away.