Heya sorry for the delay,
my system throws the following error when using exact your code:
I, [2019-03-26T18:14:26.414002 #31512-17907880] INFO -- : Started POST "/api/v1/tickets" for 666.666.666.666 at 2019-03-26 18:14:26 +0100
F, [2019-03-26T18:14:26.433990 #31512-17907880] FATAL -- :
F, [2019-03-26T18:14:26.434033 #31512-17907880] FATAL -- : ActionDispatch::Http::Parameters::ParseError (765: unexpected token at '{
"title":"Some ticket for you",
"group":"Sales",
"owner":"",
"article": {
"subject":"To-Do",
"body":"## ToDo Helpdesk ##\n\n
1. Do step one\n
Tough stuff
2. Do step two\n
2.1 even tougher\n
2.2 maybe even complicated\n
2.3 worst case - annoying\n\n
3. Do step three\n
silly work\n\n
4. Do step four\n
finally put an end to it\n",
"type":"note",
"internal":false
},
"customer":"That one guy",
"note":"Notiz",
"tags":"",
}'):
F, [2019-03-26T18:14:26.434065 #31512-17907880] FATAL -- :
F, [2019-03-26T18:14:26.434117 #31512-17907880] FATAL -- : actionpack (5.1.6.2) lib/action_dispatch/http/parameters.rb:115:in `rescue in parse_formatted_parameters'
actionpack (5.1.6.2) lib/action_dispatch/http/parameters.rb:109:in `parse_formatted_parameters'
actionpack (5.1.6.2) lib/action_dispatch/http/request.rb:361:in `block in POST'
rack (2.0.6) lib/rack/request.rb:59:in `fetch'
rack (2.0.6) lib/rack/request.rb:59:in `fetch_header'
actionpack (5.1.6.2) lib/action_dispatch/http/request.rb:360:in `POST'
actionpack (5.1.6.2) lib/action_dispatch/http/parameters.rb:53:in `parameters'
actionpack (5.1.6.2) lib/action_dispatch/http/filter_parameters.rb:41:in `filtered_parameters'
actionpack (5.1.6.2) lib/action_controller/metal/instrumentation.rb:21:in `process_action'
actionpack (5.1.6.2) lib/action_controller/metal/params_wrapper.rb:252:in `process_action'
activerecord (5.1.6.2) lib/active_record/railties/controller_runtime.rb:22:in `process_action'
actionpack (5.1.6.2) lib/abstract_controller/base.rb:124:in `process'
actionview (5.1.6.2) lib/action_view/rendering.rb:30:in `process'
actionpack (5.1.6.2) lib/action_controller/metal.rb:189:in `dispatch'
actionpack (5.1.6.2) lib/action_controller/metal.rb:253:in `dispatch'
actionpack (5.1.6.2) lib/action_dispatch/routing/route_set.rb:49:in `dispatch'
actionpack (5.1.6.2) lib/action_dispatch/routing/route_set.rb:31:in `serve'
actionpack (5.1.6.2) lib/action_dispatch/journey/router.rb:50:in `block in serve'
actionpack (5.1.6.2) lib/action_dispatch/journey/router.rb:33:in `each'
actionpack (5.1.6.2) lib/action_dispatch/journey/router.rb:33:in `serve'
actionpack (5.1.6.2) lib/action_dispatch/routing/route_set.rb:844:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/strategy.rb:192:in `call!'
omniauth (1.9.0) lib/omniauth/strategy.rb:169:in `call'
omniauth (1.9.0) lib/omniauth/builder.rb:64:in `call'
rack (2.0.6) lib/rack/etag.rb:25:in `call'
rack (2.0.6) lib/rack/conditional_get.rb:38:in `call'
rack (2.0.6) lib/rack/head.rb:12:in `call'
rack (2.0.6) lib/rack/session/abstract/id.rb:232:in `context'
rack (2.0.6) lib/rack/session/abstract/id.rb:226:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/cookies.rb:613:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/callbacks.rb:26:in `block in call'
activesupport (5.1.6.2) lib/active_support/callbacks.rb:97:in `run_callbacks'
actionpack (5.1.6.2) lib/action_dispatch/middleware/callbacks.rb:24:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/debug_exceptions.rb:59:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/show_exceptions.rb:31:in `call'
railties (5.1.6.2) lib/rails/rack/logger.rb:36:in `call_app'
railties (5.1.6.2) lib/rails/rack/logger.rb:24:in `block in call'
activesupport (5.1.6.2) lib/active_support/tagged_logging.rb:69:in `block in tagged'
activesupport (5.1.6.2) lib/active_support/tagged_logging.rb:26:in `tagged'
activesupport (5.1.6.2) lib/active_support/tagged_logging.rb:69:in `tagged'
railties (5.1.6.2) lib/rails/rack/logger.rb:24:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/remote_ip.rb:79:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/request_id.rb:25:in `call'
rack (2.0.6) lib/rack/method_override.rb:22:in `call'
rack (2.0.6) lib/rack/runtime.rb:22:in `call'
activesupport (5.1.6.2) lib/active_support/cache/strategy/local_cache_middleware.rb:27:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/executor.rb:12:in `call'
actionpack (5.1.6.2) lib/action_dispatch/middleware/static.rb:125:in `call'
rack (2.0.6) lib/rack/sendfile.rb:111:in `call'
railties (5.1.6.2) lib/rails/engine.rb:522:in `call'
railties (5.1.6.2) lib/rails/railtie.rb:185:in `public_send'
railties (5.1.6.2) lib/rails/railtie.rb:185:in `method_missing'
puma (3.11.0) lib/puma/configuration.rb:225:in `call'
puma (3.11.0) lib/puma/server.rb:624:in `handle_request'
puma (3.11.0) lib/puma/server.rb:438:in `process_client'
puma (3.11.0) lib/puma/server.rb:302:in `block in run'
puma (3.11.0) lib/puma/thread_pool.rb:120:in `block in spawn_thread'
logging (2.2.2) lib/logging/diagnostic_context.rb:474:in `block in create_with_logging_context'
So I went to search what the heck Zammad hates about parsing in that part…
Zammad parser absolutely hates you trying to use several lines… you might want to put everything in one 
So:
{
"group": "Sales",
"title": "Some ticket for you",
"owner": "",
"customer_id": 12,
"note": "Notiz",
"tags": null,
"article": {
"subject": "To-Do",
"body": "## ToDo Helpdesk ##\n\n 1. Do step one\n Tough stuff 2. Do step two\n 2.1 even tougher\n 2.2 maybe even complicated\n 2.3 worst case - annoying\n\n 3. Do step three\n silly work\n\n 4. Do step four\n finally put an end to it\n",
"type": "note",
"internal": false
}
}
Result looks like this:
When taking a look into the API-Documentation, you could also use HTML if needed, but keep it in one line. 