Our church subscribe to the Westminster Standards. But our pastor believes that not everything therein should be adhered to.
If it does, the minister should, too, or he should either agree to not teach against the parts he finds unconscionable or peacefully depart.
He does not believe in personal bible study for the members.
Very strange. And definitely out of sorts with LC 157 (not that this minister seems to feel bound to it): "The holy Scriptures are to be read with an high and reverent esteem of them; with a firm persuasion that they are the very Word of God, and that he only can enable us to understand them; with desire to know, believe, and obey the will of God revealed in them;
with diligence, and attention to the matter and scope of them; with meditation, application, self-denial, and prayer." The part I've emphasized sounds like studying to me.
According to him, that this endangers the members from errors and heresy.
It is a noble thought, but as others have mentioned, it is an error of Rome (and pretty much every cult and heretic). If he is faithfully teaching, preaching, and discipling, he should be answering questions - that interaction is a massive component of discipleship. It's pretty much the bulk of Christ's ministry. See also Paul: "Now concerning the things whereof ye wrote unto me....." (I Cor.7.1 ff.).
Furthermore,
you can develop error and heresy just as much (if not more so!) by not studying Scripture.
Moreover, he says that there is no explicit command on the Bible to study but only to meditate.
He's not technically wrong. The Bereans were commended in Acts 17 because they "received the word with all readiness, and searched the Scriptures daily, whether those things were so." This could simply mean that they did well to see if what Paul was saying about Christ was actually in the Hebrew Scriptures by reading them (which is what Christ commanded in John 5.39). There's also 2 Timothy 2.15 ("Study to show thyself approved unto God a workman that needeth not to be ashamed, dividing the word of truth aright.") but this is a command directed towards a minister. Nevertheless, there is plenty of evidence of God rewarding the studying of Scripture and asking questions by common folk. The Ethiopian eunuch in Acts 8 immediately comes to mind - yes, he was reading (v.28), but he is also studying it which leads him to have questions: "Then the Eunuch answered Philip, and said, 'I pray thee, of whom speaketh the Prophet this? of himself, or of some other man?'" (v.34) Your minister needs a slight tweak to his position - people should study the Scriptures on their own and bring their questions to the elders. This seems to fit what Peter writes in 2 Peter 1.20: "no prophecy of the Scripture is of any private interpretation."
Should I be worried or am I wrong?
You should be worried. One approach would be to talk with him directly about the matter without bringing up Scripture - simply ask institutional questions: does the congregation hold to the Westminster Standards or not, does the congregation hold to presbyterian polity or not, etc. If the answers sound like they are simply the opinions of this one minister, move on if there are other alternatives. It is also worth asking if members will be disciplined for studying Scripture on their own.