You can query the rather misleadingly named WebLink SObject to find all of the information you need about a custom button:

Select Width, Url, SystemModstamp, ShowsStatus, ShowsLocation, ScontrolId, 
RequireRowSelection, Position, PageOrSobjectType, OpenType, NamespacePrefix, Name,
MasterLabel, LinkType, LastModifiedDate, LastModifiedById, IsResizable, 
IsProtected, Id, Height, HasToolbar, HasScrollbars, HasMenubar, EncodingKey, 
DisplayType, Description, CreatedDate, CreatedById 
From WebLink
Where PageOrSObjectType = 'ObjectOfInterest__c';

You can query the rather misleadingly named WebLink SObject to find all of the information you need about a custom button:

Select Width, Url, SystemModstamp, ShowsStatus, ShowsLocation, ScontrolId, 
RequireRowSelection, Position, PageOrSobjectType, OpenType, NamespacePrefix, Name,
MasterLabel, LinkType, LastModifiedDate, LastModifiedById, IsResizable, 
IsProtected, Id, Height, HasToolbar, HasScrollbars, HasMenubar, EncodingKey, 
DisplayType, Description, CreatedDate, CreatedById 
From WebLink
Where PageOrSObjectType = 'ObjectOfInterest__c';

Edit: these aren't the droids you are looking for....this will only return information about Buttons and Links, but alas not Actions. :(

You can query the WebLink SObject to find the information you need:

Select w.Width, w.Url, w.SystemModstamp, w.ShowsStatus, w.ShowsLocation, w.ScontrolId, 
w.RequireRowSelection, w.Position, w.PageOrSobjectType, w.OpenType, w.NamespacePrefix, w.Name,
w.MasterLabel, w.LinkType, w.LastModifiedDate, w.LastModifiedById, w.IsResizable, 
w.IsProtected, w.Id, w.Height, w.HasToolbar, w.HasScrollbars, w.HasMenubar, w.EncodingKey, 
w.DisplayType, w.Description, w.CreatedDate, w.CreatedById 
From WebLink w

You can query the rather misleadingly named WebLink SObject to find all of the information you need about a custom button:

Select Width, Url, SystemModstamp, ShowsStatus, ShowsLocation, ScontrolId, 
RequireRowSelection, Position, PageOrSobjectType, OpenType, NamespacePrefix, Name,
MasterLabel, LinkType, LastModifiedDate, LastModifiedById, IsResizable, 
IsProtected, Id, Height, HasToolbar, HasScrollbars, HasMenubar, EncodingKey, 
DisplayType, Description, CreatedDate, CreatedById 
From WebLink
Where PageOrSObjectType = 'ObjectOfInterest__c';