chinese commercial space launch services was popular(even among american companies) before the us banned any american components from flying on them, at the time most satellites used some american part in one way or another so the banned cause a large fall in business, however even during that time, various companies, including european ones, choose to replace american parts with european parts to allow a chinese launch to go ahead. now chinese commercial services are recovering, in large part due to advances in chinese components and sourcing europeans ones allowing satellites to be built that are nearly as good as any american counterpart. seems people trust china just fine. in fact launch records are open for all to see, you cant hide the success or failure of a space launch and you cant hide commercial launches, those are readily available to be looked up in records.
and china has not been able to launch many deep space probes because lacks a deep space network along with enough ground stations, you wouldn't expect a guy to drive very far if there are no roads/gas stations. moreover deep space research/exploration is the 3rd rung of chinese space program, they aim to take things step by step and deep space is just not a priority yet. the first step is LEO which they've pretty much mastered, and currently they are focused on the second which is lunar exploration and further out, mars exploration. only after that does deep space come into focus. now that doesn't mean they wont do any deep space exploration/research, just that it's not a priority.
and yes that was that one argentina incident which some people seem to think is some kind of a military station, which it's not, i mean they(the locals) complained they couldn't just walk into the compound whenever they wished, therefore it must be some kind of an evil chinese military staging ground. like what? do every business just allow random people in their buildings whenever they wished in argentina? that said, china actually operates multiple ground stations, including ones in africa and pakistan, and shares various european stations under government to government agreement.