If you tacked the following filter onto the one you already have, then you'd get the output shown below:

map(select(.Address | test("^[0-9]")))

Output:

[
  {
    "Address": "1 Bridge Rd"
  }
]

For robustness, you might like to consider adding ? after the test:

map(select(.Address | test("^[0-9]")?))

Or, you could combine the two calls to map in various ways. You might like to consider:

.[].payload.address | select(test("^[0-9]")?) | {Address: .}

jq's regular expressions filters (test,match,capture) take raw text as their input. To apply a regex to key names, you'll first have to convert those key names into text.

jq provides a function to_entries for that:

cat jsonfile | jq 'to_entries'

output:

[
  {
    "key": "key11",
    "value": 1010
  },
  {
    "key": "key11_yes",
    "value": 13
  },
  {
    "key": "key11_no",
    "value": 14
  },
  {
    "key": "key12",
    "value": 12120
  },
...
]

This can then feed into a filter that extracts the key, tests it against a regexp, then either outputs the whole entry or omits it:

if (.key|test("key[0-9][0-9]$")) then ( {key: .key, value: .value } ) else empty end

The matching from_entries function can convert the remaining entries back to their original form, or with_entries can do it all in one step:

cat jsonfile|jq 'with_entries(if (.key|test("key[0-9][0-9]$")) then ( {key: .key, value: .value } ) else empty end )'

The result is all the pairs from the input whose keys matched the pattern:

{
  "key11": 1010,
  "key12": 12120,
  "key13": 12103
}

On jq 1.5, you can pass the regex to match and then get the string property of captures' second element.

jq 'match("(.*task?)\/(.*$)").captures[1].string'

You could use paths/1 instead of path because the former ignores null paths. Also with path you need to add a filter logic to ignore the null which does not match any of the regex conditions

paths(select(.name? | match("Name [0-9]")))[0]

See jq - documetation - paths/1

It's not completely clear to me what your provided script does, but it seems like it only looks for a string that contains the provided subset. I would suggest using contains or startswith. A sample script would look like:

echo "${json}" | jq --arg subnet "$subnet" '.subnets[] | select(.cidr | startswith($subnet)).id'

Since you mention regex: the latest release of jq, 1.5, includes regex support (thanks to Jeff Mercado for pointing this out!) and, if you have to deal with string manipulation problems frequently, I'd recommend checking it out.

Complement your jq pipeline with the following filter:

jq -r 'yourfilter | to_entries 
       | map(select(.key | test("^args[0-9]+")).value) | @tsv' testTab.json

The output:

tail    -f  /dev/null

Though, if you would have posted your initial testTab.json contents - I would help to optimize your current filter.