Question How to deactivate the recaptcha function completely?

Your settings are

CB for forum access.and Joomla (choose one or the other)
CB for private message and uddeIM (choose one or the other)
CB for user profiles and Kunena (choose one or the other)
CB for login.and Joomla (choose one or the other)

Now do you see why things could become problematical? Your site settings are confused. You need to "un-confuse" things.

OK, i changed the settings again, please have another look at the config:

Database collation check: The collation of your table fields are correct

Legacy mode: Disabled | Joomla! SEF: Enabled | Joomla! SEF rewrite: Enabled | FTP layer: Disabled |

This message contains confidential information

htaccess: Exists | PHP environment: Max execution time: 30 seconds | Max execution memory: 128M | Max file upload: 200M

Kunena menu details:

Warning: Spoiler!

ID	Name	Menutype	Link	Path
196	Forum	kunenamenu	view=home&defaultmenu=198	forum
197	Index	kunenamenu	view=category&layout=list&catid=0	forum/index
198	Aktuell	kunenamenu	view=topics&mode=replies	forum/aktuell
199	Neues Thema	kunenamenu	view=topic&layout=create	forum/neuesthema
200	Ohne Antwort	kunenamenu	view=topics&mode=noreplies	forum/ohneantwort
201	Meine Themen	kunenamenu	view=topics&layout=user&mode=default	forum/meinethemen
202	Profil	kunenamenu	view=user	forum/profil
203	Hilfe	kunenamenu	view=misc	forum/hilfe
204	Suche	kunenamenu	view=search	forum/suche
205	Forum	mainmenu	Itemid=196	kunena-2012-12-17

Joomla default template details : rt_metropolis | author: RocketTheme, LLC | version: 1.0 | creationdate: November 1, 2012

Kunena default template details : Blue Eagle 2.0 | author: Kunena Team | version: 2.0.4 | creationdate: 2013-01-18

Kunena version detailed: Kunena 2.0.4 | 2013-01-18 [ Pharmacopoeia ]
| Kunena detailed configuration:

Warning: Spoiler!

Kunena config settings:
board_offline	0
enablerss	1
threads_per_page	50
messages_per_page	20
messages_per_page_search	15
showhistory	1
historylimit	6
shownew	1
disemoticons	1
template	blue_eagle
showannouncement	1
avataroncat	0
catimagepath	category_images
showchildcaticon	1
rtewidth	450
rteheight	300
enableforumjump	1
reportmsg	0
username	1
askemail	0
showemail	0
showuserstats	0
showkarma	0
useredit	1
useredittime	0
useredittimegrace	600
editmarkup	1
allowsubscriptions	1
subscriptionschecked	1
allowfavorites	1
maxsubject	250
maxsig	300
regonly	1
pubwrite	0
floodprotection	0
mailmod	-1
mailadmin	-1
captcha	0
mailfull	1
allowavatarupload	0
allowavatargallery	0
avatarquality	75
avatarsize	2048
imageheight	800
imagewidth	800
imagesize	150
filetypes	txt,rtf,pdf,zip,tar.gz,tgz,tar.bz2
filesize	120
showranking	0
rankimages	0
userlist_rows	30
userlist_online	1
userlist_avatar	0
userlist_name	1
userlist_posts	0
userlist_karma	0
userlist_email	0
userlist_usertype	0
userlist_joindate	0
userlist_lastvisitdate	1
userlist_userhits	0
latestcategory	0
showstats	0
showwhoisonline	0
showgenstats	0
showpopuserstats	0
popusercount	5
showpopsubjectstats	0
popsubjectcount	5
usernamechange	0
showspoilertag	0
showvideotag	0
showebaytag	0
trimlongurls	1
trimlongurlsfront	40
trimlongurlsback	20
autoembedyoutube	1
autoembedebay	1
ebaylanguagecode	de-de
sessiontimeout	28800
highlightcode	0
rss_type	topic
rss_timelimit	week
rss_limit	100
rss_included_categories
rss_excluded_categories
rss_specification	rss2.0
rss_allow_html	1
rss_author_format	name
rss_author_in_title	1
rss_word_count	0
rss_old_titles	1
rss_cache	900
defaultpage	recent
default_sort	asc
sef	1
sefutf8	0
showimgforguest	0
showfileforguest	0
pollnboptions	4
pollallowvoteone	1
pollenabled	0
poppollscount	5
showpoppollstats	0
polltimebtvotes	00:15:00
pollnbvotesbyuser	100
pollresultsuserslist	0
maxpersotext	50
ordering_system	mesid
post_dateformat	datetime_today
post_dateformat_hover	datetime
hide_ip	1
imagetypes	jpg,jpeg,gif,png
checkmimetypes	1
imagemimetypes	image/jpeg,image/jpg,image/gif,image/png
imagequality	50
thumbheight	32
thumbwidth	32
hideuserprofileinfo	put_empty
boxghostmessage	0
userdeletetmessage	2
latestcategory_in	1
topicicons	0
debug	0
catsautosubscribed	0
showbannedreason	0
version_check	1
showthankyou	0
showpopthankyoustats	0
popthankscount	5
mod_see_deleted	0
bbcode_img_secure	text
listcat_show_moderators	1
lightbox	0
show_list_time	8
show_session_type	0
show_session_starttime	0
userlist_allowed	1
userlist_count_users	1
enable_threaded_layouts	0
category_subscriptions	post
topic_subscriptions	every
pubprofile	0
thankyou_max	10
email_recipient_count	0
email_recipient_privacy	bcc
captcha_post_limit	0
keywords	0
userkeywords	0
image_upload
file_upload
topic_layout	flat
time_to_create_page	1
show_imgfiles_manage_profile	1
hold_newusers_posts	0
hold_guest_posts	0
attachment_limit	8
pickup_category	1
article_display	intro
send_emails	1
fallback_english	1
cache	1
cache_time	60
iptracking	1
rss_feedburner_url

| Kunena integration settings:

Warning: Spoiler!

Kunena - AlphaUserPoints Disabled
Kunena - Community Builder Enabled: access=0 login=1 activity=0 avatar=0 profile=1 private=0
Kunena - Gravatar Disabled
Kunena - JomSocial Disabled
Kunena - Joomla Enabled: access=1 login=0
Kunena - Kunena Enabled: avatar=0 profile=0
Kunena - UddeIM Enabled: private=1

| Joomla! detailed language files installed:

Warning: Spoiler!

Joomla! languages installed:
de-DE	German (DE-CH-AT)
en-GB	English (United Kingdom)

Third-party components: CommunityBuilder 1.9 | UddeIM 2.8

Third-party SEF components: None

Plugins: None

Modules: None

You use maybe yet another Captcha plugin? There are some, which can be integrated in Kunena. Independent what are the Captcha settings in Kunena.
Is this not the case, then I know nothing more.

I agree with rich. Perhaps you have installed some other CAPTCHA plugin that is not affected/controlled by the Kunena configuration settings.

I looked again at the integration plugin settings (in your configuration report). According to the current settings, your current settings effectively say "don't use Community Builder avatars" and "don't use Kunena avatars". If that's what you want then that's OK. Your forum will not display any avatar images under those circumstances.

Hello rich, hello Sozzled,

yes, it is intended not to show any avatar in the forum. We do not need the avatars.
I assume, the other settings are "non-confused" now ?
I had a recaptcha Plugin installed in Joomla, but i knew this and had deactivated this plugin. To be sure that it can not have any effect on Kunena in spite of its deactivation, i deinstalled this plugin completely. But sorry, you guess the answer: the kunena recaptcha is still there.
It seems to me that we have reached the very end of possibilities in this case. Perhaps i can force the recaptcha to get out of work by making a small hack in the source code ? IF possible, please give me an advice how to do this.
Thanks for your efforts.

You have uninstalled the right plugin? There is also a plugin "Captcha - ReCaptcha", which is a part of Joomla and has no effect to Kunena.