Disclaimer: I'm a native English speaker (British English).
Yes, English speakers will eventually understand what you're trying to say by inferring it from the context, but since it's grammatically incorrect it will result in slower communication and a lot of confusion.
I'm going to demonstrate using your examples. Let's say you said "She just go shopping" instead of "She has just gone shopping." Without any context, this seems to mean "The only thing she has done is go shopping" (as opposed to going shopping and doing something else).
However, if someone asked you, "Where did she go?" and you said "She just go shopping," the listener will infer from context that she's just gone shopping, as you intended.
Again, an English speaker would understand just fine if you replied "I work for ABC for ten years" when asked "How long have you worked at ABC?", even though the sentence on its own, with no context, is difficult to make sense of.
On the other hand, if you started a conversation by saying "I work for ABC for ten years", then it's going to lead to the English-speaking listener asking questions to clarify what you mean - "When? Do you already work for them, or will you start in the future?" - because there isn't any context to what you're saying.
If you aim to communicate purely through adverbs to indicate tense, I recommend picking ones which are unambiguous, such as 'yesterday', 'tomorrow', 'soon'. Words such as 'just' have multiple, non-time-related meanings which need to be differentiated by context.