lower_bound and upper_bound set the range of primary key of items you want to retrieve. If you want to get first 10 items, then call get_table_rows by lower_bound and upper_bound with the value "", and it will return "next_key" in the result. Then pass the value of "next_key" to lower_bound (or if you want to call with "...
Eossharp doesn't contain the functionality to query the NET API and is not maintained anymore... you could just call the NET API endpoints yourself, see here https://developers.eos.io/manuals/eos/latest/nodeos/plugins/net_api_plugin/api-reference/index#operation/connections
Not sure if I understand your question but you are limiting the number of actions returned to 20 by
var resultaction = await r.GetActions(constants.LOCALCODEACCOUNT, 0, 20);
if you want more, just do
var resultaction = await r.GetActions(constants.LOCALCODEACCOUNT, 0, Int32.MaxValue);
or something similar.
You could also fetch the hole Block via the ...