neptune-client uses Python API to communicate with Neptune servers. Users are restricted to 1 thousand requests per minute. If more requests are placed, neptune-client will retry sending the data in the future (when usage does not approach the limit). In such case, users may notice some delay between the actual state of the process that executes a run and data displayed in the Neptune Web UI. The extent of this effect is proportional to the number of API calls over the 1 thousand limit.
Please consult the Pricing page, where storage limits are listed.
There are no limits. You can have as many runs and notebooks as you wish.