The only people who can perform meritorious works are those who are in the state of grace, that is to say, already saved.
Unfortunately, this isn't really the case. The Catechism, ppg. 1987 says,
"The grace of the Holy Spirit has the power to justify us, that is, to cleanse us from our sins and to communicate to us 'the righteousness of God through faith in Jesus Christ' and through Baptism."
The Bible never says that baptism, in and of itself, provides justification or grace. Instead, justification comes from Christ - from the work He did, and this grace is given when one believes on Christ. Romans 4:25 tells us that we are justified by His resurrection, in addition to being saved by His death and the shedding of His blood. I Peter 3:21 tells us that baptism is a "like figure" - a didactic picture of that real resurrection of Christ which enables us to be saved. "And through baptism" is an addition not supported by Scripture, which is therefore an additional work designed to give merit, i.e. to "earn" the grace of the Holy Spirit. Per what the Catechism says, grace is at least partially given in response to a deed (baptism), rather than the deed following the grace.
Nope. You're misreading that Scripture rather completely. It says that baptism is a "like figure" to Noah's ark (the immediately preceding reference), by which eight people "were saved through water". It continues: "This prefigures baptism, which saves you now."
Your theology of baptism is additionally mistaken in regarding baptism as something we do to somehow earn favor with God. The sacraments are something God does in every case -- he is the real celebrant and the real priest -- to confer grace on the unworthy. You can't earn baptism or deserve it any more than you can earn heaven or deserve it. It's 100% gift.