Slinza's last ability triggers whenever any creature with power 4 or greater enters, not just one you control.

Slinza's first ability doesn't change the mana cost or mana value of any spell. It changes only the total cost you pay to cast Beast spells.

Any Beasts that enter at the same time as Slinza won't enter with an additional +1/+1 counter.

If one or more static abilities that apply to a creature entering change its power, those abilities are considered when determining whether Slinza's last ability triggers. The same is true for replacement effects that apply to it, such as entering with one or more +1/+1 counters (such as the effect of Slinza's second ability, not coincidentally) or entering as a copy of another creature.

Slinza's second ability applies to all Beasts creatures you control as they enter, even if they wouldn't ordinarily enter with any +1/+1 counters on them.

Slinza's first ability can't reduce the amount of colored mana you pay for a spell. It reduces only the generic mana component of that spell.

If Slinza enters at the same time as one or more other creatures with power 4 or greater, its last ability triggers once for each of those other creatures, plus one more time for itself.

You don't choose a target for Slinza's last ability at the time it triggers. Rather, a second "reflexive" ability triggers when you pay this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.