Pronouns are omitted all the time, because Latin conjugation makes them somewhat redundant. Where the pronoun does exist, it is either emphatic or explanatory (especially necessary with third person verbs).
I speak: loquor
It is I that am speaking: ego loquor
We have killed Caesar: occidīmus Caesarem.
We, the glorious Senate of Rome, have killed Caesar: nōs, Senātus clarus Rōmae, occidīmus Caesarem.
You might have supposed she was gone: crēderēs eam abīre. [general statement]
Maybe you thought her gone, but I knew exactly where she was: tū crēderēs eam abīre, sed ego ubi adeō quō esse cognōvī. [terrible string of hiati there, pardon me for being no poet]
With third person verbs, omission of the subject will often imply a general (sometimes gnomic) statement:
They say he was once a woman: dīcunt eum fēminam olim fuisse.
The herdsman claim they are innocent: pastōrēs dīcunt eōs innōcentēs esse.
One doesn’t simply walk into Mordor: in Mordōrem nōn simpliciter iter facit.
Passive verbs omit implied subjects as well:
They fought long and hard: diū atque ācriter pūgnātum est.
The conjunctive quod sī may be translated ‘but if’ or ‘if however,’ and generally modifies or qualifies a preceding statement with a new condition. It is therefore distinction from the isolate sī, which may produce conditionals without precedent.
If Caesar arrives, we are done for: sī Caesar veneat, pereāmus. (FLV construction)
If Caesar arrives, we are done for, but if we flee, we might survive: sī Caesar veneat, pereāmus, quod sī fugiāmus, fortasse vivāmus.
Caesar is coming. However, if we flee, we might survive: Caesar venit. Quod sī fugiāmus, fortasse vivāmus.
In short, quod sī establishes a conditional in direct relation to some other fact or some other conditional.