Doubt is the enemy of faith.
I don't think it is doubt is normal, and I think that working through our doubts may often make our faith grow stronger.
Matthew says that the disciples worshipped Jesus, even though some doubted. I find that very reassuring; that we don't have to have our theology completely sorted and perfect before we can worship - or indeed before our worship is accepted. Thomas doubted, but Jesus acknowledged, and answered, those doubts - and Thomas made a great profession of faith, called the risen Jesus Lord
and God.
A man asked Jesus to heal with the words "IF you can ...." and confessed unbelief. Jesus healed.
I've often found that God meets me in my doubts, and loves me through them, rather than condemning me for them.
Was doubt not the reason Moses was barred from entering the promised land by the LORD (Numbers 20:8-12)?
I don't think that was doubt. The Lord told Moses to
speak to the rock, (v8) and Moses
struck it; sounds like disobedience to me.The Lord then told Moses he had not trusted him enough to honour him as holy, (v12). In Deut 32:51 God said that Moses would not enter the Promised Land because he had broken faith with him at the waters of Meribah, and not upheld his holiness.
Was doubt not the reason Peter sank into the sea (Matthew 14:31)?
Personally I wouldn't say that was doubt either, but I could be wrong.
Peter took his eyes off Jesus and started looking at his circumstances and the problem; I would say he started walking by sight and not by faith for a while. But maybe that's just semantics.
Jesus replied, "Truly I tell you, if you have faith and do not doubt, not only can you do what was done to the fig tree, but also you can say to this mountain, 'Go, throw yourself into the sea,' and it will be done." Matthew 21:21
Yes, maybe doubts limit what we, or the Lord can do; that doesn't mean it's wrong to have them.